
Before the Ever After
Quiz by Robert Hamann
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What does ZJ's mom do when she is worried?
She eats candy bars
She drinks coffee
She sings
When can ZJ's dad play football again?
In a month
They don't know
Never
What does ZJ's mom do when she is worried?
When can ZJ's dad play football again?
Who said that Zachariah can not drive anymore?
What happened when ZJ and his dad were doing the puzzle?
What does ZJ's mom tell Ollie's mom?
What did Zachariah ask when the watched the game on TV?
Why does ZJ keep telling Zachariah about his friends?
Are there other players who are doing strange things?
Why didn't Zachariah eat dinner with the family?
What does the new doctor think is causing all of the problems?
Why did ZJ's dad give him a guitar?
What does Zachariah call ZJ?
Here's how scientists figured out the age of the universe It took some cosmic detective work. by Passant Rabie Oct. 20, 2021 You never ask a cosmic being its age. But if that cosmic being encompasses all of space, time, and matter, you could get a little curious. Scientists have long been curious about the age of the universe and how much time has elapsed since the Big Bang. Today, scientists estimated the age of the universe to be approximately 13.8 billion years old. But how did scientists estimate how old the universe is, and are they sure of that number? It all comes down to ancient stars and the ever-expanding cosmos. How do astronomers calculate the age of the universe? To estimate the age of the universe, scientists rely on two main methods. Calculating the expansion rate of the universe Determining the ages of the oldest stars The Hubble Constant: Since its conception, the universe has been expanding at an accelerating rate. The universe’s expansion rate is known as the Hubble Constant, which is estimated at 46,200 mph per million light-years. The Hubble Constant was first calculated in the 1920s by American astronomer Edwin Hubble after discovering that several galaxies were moving away from Earth. Scientists looked to distant galaxies to measure how fast the universe was expanding. Hubble also noted that the further a galaxy was, the faster it was moving away. Based on Hubble’s observations, the astronomer came up with Hubble’s law which showed a correlation between how far an object is and the speed at which it’s receding. Using Hubble law, scientists were able to estimate the expansion rate of the universe. Scientists were then able to use the Hubble Constant to estimate the age of the universe by working backward, all the way back to the Big Bang. This extrapolation depends on the current density and composition of the universe, which shows the history of its expansion. In 2012 NASA’s Wilkinson Microwave Anisotropy Probe used that data to estimate the universe's age to be 13.772 billion years old, give or take 59 million years. A year later, The European Space Agency’s Planck spacecraft estimated the universe's age to be 13.82 billion years. Ancestral stars: Another way to determine the age of the universe is to look to the oldest stars. The universe can’t be younger than its oldest stars. Therefore, to narrow down the age of the universe, scientists measure the ages of the very first stars that formed in the cosmos. The lifecycle of a star depends on its mass, with high mass stars burning fuel at a faster rate and therefore dying out faster while low mass stars can live up to 20 billion years. Globular clusters are a dense stellar collection of around a million stars which all formed roughly around the same time. These clusters can then serve as timekeepers for the universe. By determining the masses of their stars, scientists can estimate when the globular cluster formed. The oldest globular clusters contain stars that are 0.7 times less massive than the Sun, which suggests that they are between 11 to 18 billion years old. What came before the Big Bang? Scientists can trace the universe back to its explosive birth, the Big Bang. But what happened before this theoretical birth of the cosmos? The universe may have been a singularity, all compact within a form that is smaller than a subatomic particle. It’s difficult to imagine what caused this matter to exist, but one theory even suggests that our universe was born from another universe while another imagines a series of universes being born out of one another like a formation of bubbles. Meanwhile, another theory suggests that the universe goes through an endless cycle of death and rebirth, born from its own demise. How old is the universe in seconds? If the universe is indeed cyclical, then time becomes irrelevant. But just in case you’re still attached to the modern way in which we measure the progression of life, then the age of the universe comes up to about 436,117,076,900,000,000 seconds.
1.1945-1949: The immediate years after the Second World War ● At the end of 1945, Mao Zedong had come to see the USA as the greatest threat to his aspirations. a. He understood that East Asians were looking to the USA as the true liberator from Japanese imperialism. b. The USA’s support for the Kuomintang(KMT) and the restoration of U.S. authority in formerly Japanese Manchuria clashed with the CCP’s plans to use the region for its own needs in the impending civil war between the CCP and the GMD. ■ To compound matters, while the KMT was recognised internationally as the official government in China, Mao and the CCP saw the party as a puppet of U.S. imperialism. ● While Mao saw the USA as the greater threat to the CCP’s plans, Soviet actions also frustrated him. a. The USSR provided minimal and incoherent support for the Chinese Communists in Yan’an and Manchuria. b. Stalin also attempted to extract territorial and economic concessions from the Guomindang government in the Friendship and Alliance Treaty China signed in August 1945 under American and Soviet pressure in exchange for Soviet entry into the Second World War against Japan. ● The emerging superpower conflict over Europe and over American intervention in the impending civil war in China led to Mao’s ideological perception of the 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 8 USA as an aggressive imperialist power that was hostile towards other countries, especially the USSR and China. ● In 1946, Mao promoted the theory of the intermediate zone, which envisioned a global united front against American imperialism. a. Mao saw the emerging superpower conflict as an American-Soviet contest for the intermediate zones, the capitalist, colonial and semi- colonial countries of West Europe, Africa, and Asia. b. Mao believed that the USSR was the defender of world peace. c. The intermediate zone, which included China, would not be part of the socialist camp. d. Despite the tremendous potential that U.S. aid held for China’s reconstruction, Mao’s ideological worldview and the impending civil war against the Guomindang prevented him from seeking normalised relations with the USA. In 1949, Mao decided to lean towards the side of the USSR despite two decades of unreliable support from them. e. Mao saw the anti-bourgeois campaigns in East Europe as evidence that China should isolate capitalist-bourgeois forces within it.2 f. Stalin had expelled Yugoslavia from the socialist camp as its leader, Tito was seen to have directly challenged Stalin’s authority. ■ Mao thus saw it as imperative to stress close unity to the USSR lest he was seen as a second Josip Broz Tito. At the same time, Mao sought a loose partnership with the USSR because Mao believed that China should preserve a high measure of self- reliance and zili gengsheng (自力更生) (regeneration through one’s own efforts). ● When the People’s Republic of China was formed on 1 October, 1949, relations between China’s and the USSR’s communists had improved substantially. a. However, the Chinese Communist Party (CCP) was also aware that the USSR never treated Chinese interests as a priority. What the CCP failed to fully understand was that Stalin ruled East Europe much like it was his empire and how this would have implications for China. b. In Mao’s first visit to the USSR in December 1949, Stalin was non- committal regarding the interests raised by the Chinese, and treated Mao as an underling as he feared that closer relations with the PRC would cause the USSR to lose privileges gained from the KMT. _________________________ 2 What Mao did not realise at that point was that the anti-bourgeois campaigns in East European countries were part of Stalin’s intentional design to consolidate the power of communists in them. 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 9 A note on Sino-American relations 2. Early 1950: The USA’s hands-off policy towards Taiwan begins to change ● By early 1950, the Truman administration had written off Taiwan and believed it was only a matter of time before the island fell to the PLA. ● Two events in early 1950 changed the USA’s position on East Asia. ○ The formation of the USSR-PRC alliance in February 1950 ○ The North Korean invasion of South Korea in June 1950 3. 1950: The Sino-Soviet Friendship, Alliance and Mutual Assistance Treaty ● Signed on 14 February, 1950. 3.1Implications for Sino-Soviet relations ● Stalin saw it as a means to get concessions that he had failed to get from the Kuomintang (KMT) government in 1945. ● For Mao and the newly founded People’s Republic of China (PRC), the alliance would provide security against U.S. imperialism and allow the PRC to get economic aid for reconstruction from the USSR. ● The Chinese realised soon after the 1950 treaty had been signed that the Soviet Union was intent on exploiting the agreement in its own favour. 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 10 ● The Sino-Soviet alliance was officially directed against Japanese militarism and its allies, especially the USA. ● The Sino-Soviet alliance comprised three elements: party, military and economic relations. ○ Party: The Chinese Communist Party (CCP) was included in the customs of communist party internationalism, such as regular exchange of party delegations to congresses of the fraternal parties in Stalin’s socialist camp. ■ This move was meant to bring the PRC’s ideological beliefs about communism into greater alignment with the USSR’s. ○ Military: The alliance was supposed to provide the newly formed and weak PRC with a strategic deterrent and military aid against the USA on three fronts: Guomindang-held Taiwan, divided Korea, and Vietnam where France attempted to reestablish its colonial control. ■ Convinced that the USA would aggressively seek ways to undermine the CCP-led PRC through Taiwan, Korea and Vietnam, Mao sought an active defence. ● While in Moscow, Mao unsuccessfully asked Stalin to provide military assistance for the liberation of Taiwan. ● At the beginning of 1950, the PRC delivered large-scale military aid to Hanoi. The PRC was the first country to grant the communist-led Democratic Republic of Vietnam diplomatic recognition on 18 January 1950; Mao persuaded Stalin to do so on 30 January 1950. ● The PRC committed itself to North Korea, where Mao saw the commitment to North Korea both as a defence against U.S. imperialism and as support for a fellow communist country. ○ Economic: During Mao’s first stay in Moscow, Stalin had personally promised the delivery of fifty projects for primary industrialisation. ■ The agreement also led to a series of supplementary ones, such as a US$ 300 million loan that the PRC would repay with a mixture of strategic materials, rubber, agricultural products, goods for daily use and hard currency. ■ Significantly, Stalin used Soviet military and economic aid to extract concessions similar to those he failed to get from the Guomindang government in 1945. ■ The USSR and PRC would disagree on the pace and extent of the PRC’s planned development. ● In the last five weeks of Stalin’s life in early 1953, he attempted to pressure the PRC to reduce the planned 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 11 development speed to a mere annual growth of 13-14 percent, and to plan individual projects in detail beforehand. These moves would potentially result in the PRC’s economy growing at a slower rate than initially projected. ● However, after Stalin’s death on 5 March 1953, the PRC’s Zhou Enlai decided to use his visit of condolence to the USSR to press forward negotiations. ○ When talks resumed in 1 April 1953, Beijing pressed for 150 Soviet industrial projects, but Moscow reduced them to 91 on the basis of insufficient data provided by the Chinese. ■ The economic disarray after China’s civil war and the economic pressures that came with the Korean War influenced recovery and reconstruction in the early years of the PRC. ● Despite the PRC being unable to tap into Soviet economic assistance immediately, mutual trade between China and the USSR nevertheless increased 6.5 times from 1950 to 1956. ● Together with the 50 projects promised by Stalin in 1950, the final version of the First FYP for the PRC included 141 Soviet and 68 East European projects in a total of 649 planned. Three thousand Soviet advisers sent to China in subsequent years were directly linked to the First FYP. ● By 1955, over 60 percent of China’s goods exchange was with the USSR. ● Soviet economic assistance to China added up to the largest foreign development venture in the socialist camp ever. ○ The total number of planned projects amounted to between 300 and 360 projects. ○ However, the number of total finished projects ranged between 134 and 150. ● Transfers of knowledge and expertise were important to China’s economic development. ○ A study on Soviet experts counts 1,445 political advisers and 9,313 technical specialists sent to China until their sudden withdrawal in mid-1960. ■ For political reasons, the gradual withdrawal of advisers began after late 1956.
Smallpox epidemics had struck the tribes of the Upper Missouri at least twice before the terrible epidemic of 1837. The earlier epidemics of 1781 and 1801 took the lives of thousands of Mandans, Hidatsas, and Arikaras and forced them to move north to re-build their villages near the mouth of the Knife River. However, not long after the earthlodge villages became established on the Knife, they experienced the worst smallpox epidemic ever. Fort Clark was a fur-trading post that had been built in 1823 just a few miles south of the mouth of the Knife River on the west bank of the Missouri River. One-quarter mile from the fort was the Mandan village of Mitu'tahakto's (meh TOOT ah hahnk tosh). Within 15 miles of the post were several more Mandan, Arikara, and Hidatsa villages. Earlier epidemics and inter-tribal conflict had forced the earthlodge peoples north to the Knife River. The Yanktonais, Crows, Assiniboines and other tribes traveled to Fort Clark bringing buffalo robes and furs to trade for tobacco, guns, cloth, and other goods. Fort Clark was a busy, densely populated center of international trade. On June 18, 1837, the steamboat St. Peters approached Fort Clark. In addition to supplies, the St. Peters brought Andrew Jackson Chardon, the two-year-old son of Fort Clark’s superintendent, Francis Chardon. Chardon met the boat some 30 miles downstream. He removed his son from the boat and heard the news that people on the boat were infected with smallpox. When the steamboat landed at Fort Clark, people came and went from the boat to the fort and the villages. Workers from the boat and the post unloaded goods and loaded bales of furs. All of the activity took place in less than 24 hours amid a “frolick” of singing and dancing and celebration. Once loaded, the St. Peters headed upstream to Fort Union carrying the deadly virus. On July 14, 1837, Chardon noted in his journal that a Mandan man had died of smallpox in the village. (See Document 2.) Chardon knew that smallpox would become an epidemic and that many more would die, but the extent of the epidemic stunned him. He recorded the deaths of important village leaders including the highly-respected second chief of the Mandans, Four Bears. He heard, probably second-hand, the death-speech of Four Bears (See Document 2, entry for July 30.) and recorded it in his journal. Chardon was unable to keep track of the number of deaths: “they die so fast that it is impossible,” he wrote. Survivors swore revenge against Chardon for bringing death to their villages. There were murders and threats of murder as the deeply despairing Mandans tried to avenge the deaths of their families and friends. Some people, sick with smallpox or feeling desperate from the loss of every member of their family, committed suicide. Suicide was unknown among the Mandans and Hidatsas before the epidemic. Before the disease reached the post, Chardon sent his oldest son downriver to Fort Pierre. The boy was sent on to his grandparents’ home in Pennsylvania. The younger son, Andrew Jackson, remained with Chardon (the boy’s mother had died in April before the epidemic). When the disease finally penetrated the walls of the fort, Andrew Jackson sickened and died as did many other young children of the post employees. When the disease reached Fort Union, more people, both Indians and non-Indians, were exposed and suffered. The superintendent at Fort Union tried to inoculate as many people as he could. Many tribes fled the area and probably saved many lives in doing so. The disease however, continued to spread across the northern Great Plains where the Indians had been denied access to the 1832 federal vaccination program. The Mandan people suffered the greatest losses in the epidemic. Frequent, close contact among the people of the villages and the fur trade post helped to spread the disease quickly. About 2,000 Mandans lived in the Knife River villages in the spring of 1837. By October, 138 people remained alive. The survivors moved from the village at Fort Clark to other villages. The Arikaras, who had lost perhaps two-thirds of their population, moved into Mitu'tahakto's. They harvested the Mandans’ garden crops that year and remained in the village near Fort Clark.
She went by the name of Belisa Crepusculario, not because she had been baptized with that name or given it by her mother, but because she herself had searched until she found the poetry of "beauty" and "twilight" and cloaked herself in it. She made her living selling words. She journeyed through the country from the high cold mountains to the burning coasts, stopping at fairs and in markets where she set up four poles covered by a canvas awning under which she took refuge from the sun and rain to minister to her customers. She did not have to peddle her merchandise because from having wandered far and near, everyone knew who she was. Some people waited for her from one year to the next, and when she appeared in the village with her bundle beneath her arm, they would form a line in front of her stall. Her prices were fair. For five centavos she delivered verses from memory, for seven she improved the quality of dreams, for nine she wrote love letters, for twelve she invented insults for irreconcilable enemies. She also sold stories, not fantasies but long, true stories she recited at one telling, never skipping a word. This is how she carried news from one town to another. People paid her to add a line or two: our son was born, so-and-so died, our children got married, the crops burned in the field. Wherever she went a small crowd gathered around to listen as she began to speak, and that was how they learned about each others' doings, about distant relatives, about what was going on in the civil war. To anyone who paid her fifty centavos in trade, she gave the gift of a secret word to drive away melancholy. It was not the same word for everyone, naturally, because that would have been collective dece it. Each person received his or her own word, with the assurance that no one else would use it that way in this universe or the Beyond. Belisa Crepusculario had been born into a family so poor they did not even have names to give their children. She came into the world and grew up in an inhospitable land where some years the rains became avalanches of water that bore everything away before them and others when not a drop fell from the sky and the sun swelled to fill the horizon and the world became a desert. Until she was twelve, Belisa had no occupation or virtue other than having withstood hunger and the exhaustion of centuries. During one interminable drought, it fell to her to bury four younger brothers and sisters, when she realized that her turn was next, she decided to set out across the 2 plains in the direction of the sea, in hopes that she might trick death along the way. The land was eroded, split with deep cracks, strewn with rocks, fossils of trees and thorny bushes, and skeletons of animals bleached by the sun. From time to time she ran into families who, like her, were heading south, following the mirage of water. Some had begun the march carrying their belongings on their back or in small carts, but they could barely move their own bones, and after a while they had to abandon their possessions. They dragged themselves along painfully, their skin turned to lizard hide and their eyes burned by the reverberating glare. Belisa greeted them with a wave as she passed, but she did not stop, because she had no strength to waste in acts of compassion. Many people fell by the wayside, but she was so stubborn that she survived to cross through that hell and at long last reach the first trickles of water, fine, almost invisible threads that fed spindly vegetation and farther down widened into small streams and marshes. Belisa Crepusculario saved her life and in the process accidentally discovered writing. In a village near the coast, the wind blew a page of newspaper at her feet. She picked up the brittle yellow paper and stood a long while looking at it, unable to determine its purpose, until curiosity overcame her shyness. She walked over to a man who was washing his horse in the muddy pool where she had quenched her thirst. "What is this?" she asked. "The sports page of the newspaper," the man replied, concealing his surprise at her ignorance. The answer astounded the girl, but she did not want to seem rude, so she merely inquired about the significance of the fly tracks scattered across the page. "Those are words, child. Here it says that Fulgencio Barba knocked out El Negro Tiznao in the third round." That was the day Belisa Crepusculario found out that words make their way in the world without a master, and that anyone with a little cleverness can appropriate them and do business with them. She made a quick assessment of her situation and concluded that aside from becoming a prostitute or working as a servant in the kitchens of the rich there were few occupations she was qualified for. It seemed to her that selling words would be an honorable alternative. From that moment on, she worked at that profession, and was never tempted by any other. At the beginning, she offered her merchandise unaware that words could be written outside of newspapers. When she learned otherwise, she calculated the infinite possibilities of her trade and with her savings paid a priest twenty pesos to teach her to read and write, with her three 3 remaining coins she bought a dictionary. She poured over it from A to Z and then threw it into the sea, because it was not her intention to defraud her customers with packaged words. One August morning several years later, Belisa Crepusculario was sitting in her tent in the middle of a plaza, surrounded by the uproar of market day, selling legal arguments to an old man who had been trying for sixteen years to get his pension. Suddenly she heard yelling and thudding hoofbeats. She looked up from her writing and saw, first, a cloud of dust, and then a band of horsemen come galloping into the plaza. They were the Colonel's men, sent under orders of El Mulato, a giant known throughout the land for the speed of his knife and his loyalty to his chief. Both the Colonel and El Mulato had spent their lives fighting in the civil war, and their names were ineradicably linked to devastation and calamity. The rebels swept into town like a stampeding herd, wrapped in noise, bathed in sweat, and leaving a hurricane of fear in their trail. Chickens took wing, dogs ran for their lives, women and children scurried out of sight, until the only living soul left in the market was Belisa Crepusculario. She had never seen El Mulato and was surprised to see him walking toward her. "I'm looking for you," he shouted, pointing his coiled whip at her, even before the words were out, two men rushed her -- knocking over her canopy and shattering her inkwell -- bound her hand and foot, and threw her like a sea bag across the rump of El Mulato's mount. Then they thundered off toward the hills. Hours later, just as Belisa Crepusculario was near death, her heart ground to sand by the pounding of the horse, they stopped, and four strong hands set her down. She tried to stand on her feet and hold her head high, but her strength failed her and she slumped to the ground, sinking into a confused dream. She awakened several hours later to the murmur of night in the camp, but before she had time to sort out the sounds, she opened her eyes and found herself staring into the impatient glare of El Mulato, kneeling beside her. "Well, woman, at last you've come to," he said. To speed her to her senses, he tipped his canteen and offered her a sip of liquor laced with gunpowder. She demanded to know the reason for such rough treatment, and El Mulato explained that the Colonel needed her services. He allowed her to splash water on her face, and then led her to the far end of the camp where the most feared man in all the land was lazing in a hammock strung between two trees. She could not see his face, because he lay in the deceptive shadow of the leaves and the indelible shadow of all his years as a bandit, but she imagined from the way his 4 gigantic aide addressed him with such humility that he must have a very menacing expression. She was surprised by the Colonel's voice, as soft and well-modulated as a professor's. "Are you the woman who sells words?" he asked. "At your service," she stammered, peering into the dark and trying to see him better. The Colonel stood up, and turned straight toward her. She saw dark skin and the eyes of a ferocious puma, and she knew immediately that she was standing before the loneliest man in the world. "I want to be President," he announced. The Colonel was weary of riding across that godforsaken land, waging useless wars and suffering defeats that no subterfuge could transform into victories. For years he had been sleeping in the open air, bitten by mosquitoes, eating iguanas and snake soup, but those minor inconveniences were not why he wanted to change his destiny. What truly troubled him was the terror he saw in people's eyes. He longed to ride into a town beneath a triumphal arch with bright flags and flowers everywhere, he wanted to be cheered, and be given newly laid eggs and freshly baked bread. Men fled at the sight of him, children trembled, and women miscarried from fright, he had had enough, and so he had decided to become President. El Mulato had suggested that they ride to the capital, gallop up to the Palace, and take over the government, the way they had taken so many other things without anyone's permission. The Colonel, however, did not want to be just another tyrant, there had been enough of those before him and, besides, if he did that, he would never win people's hearts. It was his aspiration to win the popular vote in the December elections. "To do that, I have to talk like a candidate. Can you sell me the words for a speech?" the Colonel asked Belisa Crepusculario. She had accepted many assignments, but none like this. She did not dare refuse, fearing that El Mulato would shoot her between the eyes, or worse still, that the Colonel would burst into tears. There was more to it than that, however, she felt the urge to help him because she felt a throbbing warmth beneath her skin, a powerful desire to touch that man, to fondle him, to clasp him in her arms. All night and a good part of the following day, Belisa Crepusculario searched her repertory for words adequate for a presidential speech, closely watched by El Mulato, who could not take his eyes from her firm wanderer's legs and virginal breasts. She discarded harsh, cold words, words 5 that were too flowery, words worn from abuse, words that offered improbable promises, untruthful and confusing words, until all she had left were words sure to touch the minds of men and women's intuition. Calling upon the knowledge she had purchased from the priest for twenty pesos, she wrote the speech on a sheet of paper and then signaled El Mulato to untie the rope that bound her ankles to a tree. He led her once more to the Colonel, and again she felt the throbbing anxiety that had seized her when she first saw him. She handed him the paper and waited while he looked at it, holding it gingerly between thumbs and fingertips. "What the shit does this say," he asked finally. "Don't you know how to read?" "War's what I know," he replied. She read the speech aloud. She read it three times, so her client could engrave it on his memory. When she finished, she saw the emotion in the faces of the soldiers who had gathered round to listen, and saw that the Colonel's eyes glittered with enthusiasm, convinced that with those words the presidential chair would be his. "If after they've heard it three times, the boys are still standing there with their mouths hanging open, it must mean the thing's damn good, Colonel" was El Mulato's approval. "All right, woman. How much do I owe you?" the leader asked. "One peso, Colonel." "That's not much," he said, opening the pouch he wore at his belt, heavy with proceeds from the last foray. "The peso entitles you to a bonus. I'm going to give you two secret words," said Belisa Crepusculario. "What for?" She explained that for every fifty centavos a client paid, she gave him the gift of a word for his exclusive use. The Colonel shrugged. He had no interest at all in her offer, but he did not want to be impolite to someone who had served him so well. She walked slowly to the leather stool where he was sitting, and bent down to give him her gift. The man smelled the scent of a mountain cat issuing from the woman, a fiery heat radiating from her hips, he heard the terrible whisper of her hair, and a breath of sweetmint murmured into his ear the two secret words that were his alone. "They are yours, Colonel," she said as she stepped back. "You may use them as much as you 6 please." El Mulato accompanied Belisa to the roadside, his eyes as entreating as a stray dog's, but when he reached out to touch her, he was stopped by an avalanche of words he had never heard before; believing them to be an irrevocable curse, the flame of his desire was extinguished. During the months of September, October, and November the Colonel delivered his speech so many times that had it not been crafted from glowing and durable words it would have turned to ash as he spoke. He travelled up and down and across the country, riding into cities with a triumphal air, stopping in even the most forgotten villages where only the dump heap betrayed a human presence, to convince his fellow citizens to vote for him. While he spoke from a platform erected in the middle of the plaza, El Mulato and his men handed out sweets and painted his name on all the walls in gold frost. No one paid the least attention to those advertising ploys; they were dazzled by the clarity of the Colonel's proposals and the poetic lucidity of his arguments, infected by his powerful wish to right the wrongs of history, happy for the first time in their lives. When the Candidate had finished his speech, his soldiers would fire their pistols into the air and set off firecrackers, and when finally they rode off, they left behind a wake of hope that lingered for days on the air, like the splendid memory of a comet's tail. Soon the Colonel was the favorite. No one had ever witnessed such a phenomenon: a man who surfaced from the civil war, covered with scars and speaking like a professor, a man whose fame spread to every corner of the land and captured the nation's heart. The press focused their attention on him. Newspapermen came from far away to interview him and repeat his phrases, and the number of his followers and enemies continued to grow. "We're doing great, Colonel," said El Mulato, after twelve successful weeks of campaigning. But the Candidate did not hear. He was repeating his secret words, as he did more and more obsessively. He said them when he was mellow with nostalgia; he murmured them in his sleep; he carried them with him on horseback; he thought them before delivering his famous speech; and he caught himself savoring them in his leisure time. And every time he thought of those two words, he thought of Belisa Crepusculario, and his senses were inflamed with the memory of her feral scent, her fiery heat, the whisper of her hair, and her sweetmint breath in his ear, until he began to go around like a sleepwalker, and his men realized that he might die before he ever sat in the presidential chair. "What's got hold of you, Colonel," El Mulato asked so often that finally one day his chief broke 7 down and told him the source of his befuddlement: those two words that were buried like two daggers in his gut. "Tell me what they are and maybe they'll lose their magic," his faithful aide suggested. "I can't tell them, they're for me alone," the Colonel replied. Saddened by watching his chief decline like a man with a death sentence on his head, El Mulato slung his rifle over his shoulder and set out to find Belisa Crepusculario. He followed her trail through all that vast country, until he found her in a village in the far south, sitting under her tent reciting her rosary of news. He planted himself, spraddle-legged, before her, weapon in hand. "You! You're coming with me," he ordered. She had been waiting. She picked up her inkwell, folded the canvas of her small stall, arranged her shawl around her shoulders, and without a word took her place behind El Mulato's saddle. They did not exchange so much as a word in all the trip; El Mulato's desire for her had turned into rage, and only his fear of her tongue prevented his cutting her to shreds with his whip. Nor was he inclined to tell her that the Colonel was in a fog, and that a spell whispered into his ear had done what years of battle had not been able to do. Three days later they arrived at the encampment, and immediately, in view of all the troops, El Mulato led his prisoner before the Candidate. "I brought this witch here so you can give her back her words, Colonel," El Mulato said, pointing the barrel of his rifle at the woman's head. "And then she can give you back your manhood." The Colonel and Belisa Crepusculario stared at each other, measuring one another from a distance. The men knew then that their leader would never undo the witchcraft of those accursed words, because the whole world could see the voracious-puma eyes soften as the woman walked to him and took his hand in hers. Copyright © 1989 by Isabel Allende From The Stories of Eva Luna, Translated by Margaret Sayers Peden
Princess Julian and Sutan Rumandung Long ago, there lived a king named Tuanku Raja Kecik. He wished to find a husband for his beloved granddaughter, Princess Julian. Therefore, he held a big party, inviting all young men in the kingdom . One night before the royal party, Princess Julian had a strange dream. In the dream, she met a young man named Sutan Rumandung. She believed deep in her heart that this man would be her future husband. Day after day, the party went on, but no one named Sutan Rumandung appeared. On the very last day, a ship arrived at the harbor, led by a young, handsome captain. Hearing the news, the king’s soldiers brought the young captain to the palace. In that moment, Princess Julian saw him, she realized that he was the same man from her dream. And it was true — the young man introduced himself as Sutan Rumandung. Knowing this, the king’s family was overjoyed, and soon the two were engaged. Before leaving to continue his voyage, Sutan Rumandung made a promise: if he married another woman, he would sink with his ship. Princess Julian also made a promise: if she married another man, she would turn into a white siamang. Days turned into months, and months into years. For two years, Princess Julian waited, but no message ever came. In the third year, another grand ship docked at the harbor. The captain was handsome and noble, and slowly, Princess Julian’s heart turned toward him. He too fell in love with her, and they decided to marry. On the wedding day, when the priest asked her for her answer, Princess Julian suddenly screamed — a cry like a siamang’s. Before everyone’s eyes, her body changed into a white siamang. The king could only watch, knowing the curse of her broken promise had come true. Not long after, the villagers found the white siamang lifeless in a tree. Soon came the news: Sutan Rumandung had died, his ship sinking into the sea. He, too, had broken his promise. And so ended the tragic tale of two lovers who betrayed each other.
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: • Free-falling objects do not encounter air resistance. • All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs • Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: • An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. • If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.
Commas Directions: Correct the sentences by adding commas where needed. 1. After the sound of the bell we realized it was a false alarm. 2. Mr. Yoshino the head of the department resigned yesterday. 3. The gentleman with the black umbrella who is an ambassador to the United States said hello to us as we were entering the hotel. 4. Even though we won the game the players unfortunately did not play their best. 5. Heather walked quickly up to the door and knocked hoping that someone would answer. Author’s Purpose 6. An author writes a story about a boy who saves his town from a flood by using his quick thinking. The author includes exciting descriptions of the boy's bravery. What is the author’s most likely purpose for writing this story? A. To inform readers about the dangers of floods B. To entertain readers with a heroic tale C. To explain how to prevent floods D. To persuade readers to prepare for emergencies 7. Which of the following is an example of an author writing to persuade? A. A science textbook chapter explaining the water cycle B. A commercial encouraging people to adopt shelter pets C. A short story about a girl who finds a magical necklace D. A recipe for making chocolate chip cookies 8. Read the following sentence: "Studies show that students who read for 20 minutes a day score higher on tests. Reading is one of the best habits you can develop for success in school and life." What is the author’s purpose in this passage? A. To entertain readers with a fun story B. To persuade readers to read more often C. To inform readers about how books are written D. To explain how to find books to read 9. An author writes a how-to guide titled 10 Easy Steps to Plant a Garden. What is the author’s primary purpose? A. To persuade readers to grow their own vegetables B. To inform readers how to plant a garden C. To entertain readers with funny garden tips 10. Read the excerpt: "Long ago, in a village surrounded by mountains, the people discovered a secret about their water well. Every full moon, the well water turned to gold for just one night. But no one knew why. This mystery brought travelers from far and wide, hoping to uncover the truth." What is the author’s purpose in this excerpt? A. To persuade readers to visit the village B. To inform readers about a historical event C. To entertain readers with a mysterious tale D. To explain the science behind the water Main Idea When I stepped out into the bright sunlight from the darkness of the movie house, I had only two things on my mind: Paul Newman and a ride home. I was wishing I looked like Paul Newman--- he looks tough and I don't--- but I guess my own looks aren't so bad. I have light-brown, almost-red hair and greenish-gray eyes. I wish they were more gray because I hate most guys that have green eyes, but I have to be content with what I have. My hair is longer than a lot of boys wear theirs, squared off in back and long at the front and sides, but I am a greaser and most of my neighborhood rarely bothers to get a haircut. Besides, I look better with long hair. 11. What is the main idea? The narrator likes movies. The narrator wishes he was Paul Newman. The narrator is content with his appearance. The narrator looks better with long hair. 12. The narrator believes. . . looks are important. he should get a haircut. green eyes are bad. that he has red hair. Once there were four girls who shared a pair of pants. The girls were all different sizes and shapes, and yet the pants fit each of them. You may think this is a suburban myth. But I know it's true, because I am one of them, one of the sisters of the Traveling Pants. We discovered their magic last summer, purely by accident. The four of us were splitting up for the first time in our lives. Carmen had gotten them from a secondhand place without even bothering to try them on. She was going to throw them away, but by chance, Tibby spotted them. First Tibby tried them; then me, Lena; then Bridget; then Carmen. By the time Carmen pulled them on, we knew something extraordinary was happening. If the same pants fit and I mean really fit the four of us, they aren't ordinary. They don't belong completely to the world of things you can see and touch. My sister, Effie, claims I don't believe in magic, and maybe I didn't then. But after the first summer of the Traveling Pants, I do. 13. What is the main idea? Four friends were connected through a special pair of pants. A pair of pants called the Traveling Pants. Carmen finding a pair of pants from a second-hand shop. The girls believing in magic. 14. The narrator included that the pants fit all of them to emphasize how the girls become friends. the girls are different sizes. why the pants are special. where the pants came from. If you are interested in stories with happy endings, you would be better off reading some other book. In this book, not only is there no happy ending, there is no happy beginning and very few happy things in the middle. This is because not very many happy things happened in the lives of the three Baudelaire youngsters. Violet, Klaus, and Sunny Baudelaire were intelligent children, and they were charming, and resourceful, and had pleasant facial features, but they were extremely unlucky, and most everything that happened to them was rife with misfortune, misery, and despair. I'm sorry to tell you this, but that is how the story goes. 15. What is the main idea? description about the story to come. A warning about the story and its sad content. A declaration about the Baudelaire family. A beginning for the end of the story. 16. The narrator believes the reader does not like sad stories. likes stories with happy endings. can’t enjoy the story. will find the story unhappy. 17. Read the following sentence: Of course you can exaggerate your story, but what you say must be based on truth. Which word means the same as exaggerate? repeat reveal overstate increase 18. What is the meaning of the word inaugurated, used in the following sentence: Less than two months after Abraham Lincoln was inaugurated President in 1861, he encountered one of the most difficult tasks ever experienced by a United States leader: civil war. elected by a vote brought into office identified by name viewed as an authority 19. What does the phrase “practice your presentation so much that you could do it in your sleep” suggest in the following sentence: The best advice is to practice your presentation so much that you could do it in your sleep. get plenty of sleep the night before giving a presentation give their presentations in front of a small audience first take advice from their teachers on how to write a presentation memorize their presentations before they give them 20. Read the following sentence: The Phoenix Mars Lander is a NASA spacecraft that landed on the Red Planet in May 2009 to study the history of water and potential for life on the planet. What is another word for potential? existence situation possibility qualification
TECH FREE! by Sam Winton Have you ever wondered what it would be like to give up technology? I'm a TV journalist and I spend a lot of my working life in front of a computer or a TV. I decided to conduct my own private experiment: I would spend a day trying to manage without technological devices. What a scary thought! The first thing I usually do every day is reach for my smartphone to check the time and read any messages or emails. But I'd locked it away in a drawer the night before. Already I was feeling very cut off from the world, and it was only... actually, I had no idea what time it was! After breakfast, I needed to get some cash. Inevitably, this meant a trip to the bank because cash points are technological devices. I had to queue, but I had a very nice conversation with a woman whilst I was waiting. Not surprisingly, the bank teller thought I was a bit strange withdrawing money this way. I think she thought I was a robber! Then it was on to the supermarket. You may be wondering what's technological about that. Well, I had to make sure I avoided the self-service check-out and joined the queue for a normal one - with a real person. Naturally, it took longer, but I had a great chat with the guy who served me, and he told me about a new club that is opening up nearby. Would I have found out about that if I'd gone to the self- service check-out? No. Afterwards, I came home to have a go at writing a news story by hand. Strangely, I found it easier to concentrate on my writing. But my hand and fingers got really sore! And I have to confess - by this stage, I was having to make a real effort not to get my phone out and check my messages. I was starting to wonder what my friends were doing. Maybe they were making plans to go to that new club, and I would never know! All in all, I wouldn't say I could live without technology. Predictably, I really missed my phone all day. The worst part was not being able to check updates in the news or from my friends. I felt very out of touch. However, I kept to my promise of a tech-free day and I did have more face-to-face interaction. Undoubtedly, it made me realise just how addicted to technology we all are.