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Writing the first half of a biography about Darwin and his theory of evolution
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Early society and accomplishments Origins Knowledge of the early prehistory of Southeast Asia has undergone exceptionally rapid change as a result of archaeological discoveries made since the 1960s, although the interpretation of these findings has remained the subject of extensive debate. Nevertheless, it seems clear that the region has been inhabited from the earliest times. Hominid fossil remains date from approximately 1,500,000 years ago and those of Homo sapiens from approximately 40,000 years ago. Furthermore, until about 7000 bce the seas were some 150 feet (50 metres) lower than they are now, and the area west of Makassar Strait consisted of a web of watered plains that sometimes is called Sundaland. These land connections perhaps account for the coherence of early human development observed in the Hoabinhian culture, which lasted from about 13,000 to 5000 or 4000 bce. The stone tools used by hunting and gathering societies across Southeast Asia during this period show a remarkable degree of similarity in design and development. When the sea level rose to approximately its present level about 6000 bce, conditions were created for a more variegated environment and, therefore, for more extensive differentiation in human development. While migration from outside the region may have taken place, it did not do so in a massive or clearly punctuated fashion; local evolutionary processes and the circulation of peoples were far more powerful forces in shaping the region’s cultural landscape. Technological developments and population expansion Perhaps because of a particular combination of geophysical and climatic factors, early Southeast Asia did not develop uniformly in the direction of increasingly complex societies. Not only have significant hunting and gathering populations continued to exist into the 21st century, but the familiar cultural sequences triggered by such events as the discovery of agriculture or metallurgy do not seem to apply. This is not to say that the technological capabilities of early Southeast Asian peoples were negligible, for sophisticated metalworking (bronze) and agriculture (rice) were being practiced by the end of the 3rd millennium bce in northeastern Thailand and northern Vietnam, and sailing vessels of advanced design and sophisticated navigational skills were spread over a wider area by the same time or earlier. Significantly, these technologies do not appear to have been borrowed from elsewhere but were indigenous and distinctive in character. Austronesian languages Austronesian languagesMajor divisions of the Austronesian languages. These technological changes may partially account for two crucial developments in Southeast Asia’s later prehistory. The first is the extraordinary seaborne expansion of speakers of Proto-Austronesian languages and their descendants, speakers of Austronesian (or Malayo-Polynesian) languages, which occurred over a period of 5,000 years or more and came to encompass a vast area and to stretch nearly half the circumference of Earth at the Equator. This outward movement of people and culture was evolutionary rather than revolutionary, the result of societal preference for small groups and a tendency of groups to hive off once a certain population size had been reached. It began as early as 4000 bce, when Taiwan was populated from the Asian mainland, and subsequently it continued southward through the northern Philippines (3rd millennium bce), central Indonesia (2nd millennium bce), and western and eastern Indonesia (2nd and 1st millennia bce). From approximately 1000 bce on the expansion continued both eastward into the Pacific, where that immense region was populated in a process continuing to about 1000 ce as voyagers reached the Hawaiian Islands and New Zealand, and westward, where Malay peoples reached and settled the island of Madagascar sometime between 500 and 700 ce, bringing with them (among other things) bananas, which are native to Southeast Asia. Thus, for a considerable period of time, the Southeast Asian region contributed to world cultural history, rather than merely accepting outside influences, as frequently has been suggested. The second development, which began possibly as early as 1000 bce, centred on the production of fine bronze and the fashioning of bronze-and-iron objects, particularly as they have been found at the site in northern Vietnam known as Dong Son. The earliest objects consisted of socketed plowshares and axes, shaft-hole sickles, spearheads, and such small items as fishhooks and personal ornaments. By about 500 bce the Dong Son culture had begun producing the bronze drums for which it is known. The drums are large objects (some weigh more than 150 pounds [70 kg]), and they were produced by the difficult lost-wax casting process and decorated with fine geometric shapes and depictions of animals and humans. This metal industry was not derived from similar industries in China or India. Rather, the Dong Son period offers one of the most powerful—though not necessarily the only or earliest—examples of Southeast Asian societies transforming themselves into more densely populated, hierarchical, and centralized communities. Since typical drums, either originals or local renditions, have been found throughout Southeast Asia and since they are associated with a rich trade in exotics and other goods, the Dong Son culture also suggests that the region as a whole consisted not of isolated, primitive niches of human settlement but of a variety of societies and cultures tied together by broad and long-extant trading patterns. Although none of these societies possessed writing, some displayed considerable sophistication and technological skill, and, although none appears to have constituted a territorial centralized state, new and more complex polities were forming.
Classroom Expectations and Policies Assessment 1. What should students bring to class every day? a. Only a positive attitude b. Charged Chromebook, writing utensil, and positive attitude c. Just their books d. Snacks and drinks 2. What is the consequence for bullying in the classroom? a. A warning b. A violation card c. Extra homework d. A meeting with the principal 3. If a student breaks a personal item, what must they do? a. Ignore it b. Apologize c. Buy a new one for the teacher d. Ask for forgiveness 4. How should students handle using the futon during class? a. Sit on it every day b. Use it without asking c. Ask first and only use it during work time d. Sit on it during lectures 5. Where will all assignments be posted? a. On the classroom wall b. On Canvas c. Only verbally d. In a textbook 6. What happens if an assignment is submitted late? a. It will be graded normally b. It will not be accepted c. It will drop a letter grade each day it is late d. It will be given extra credit 7. After how many days of lateness will a student receive only half credit for an assignment? a. 1 day b. 2 days c. 3 days d. 4 days 8. What is the policy for retaking tests? a. No retakes allowed b. Students must schedule the retake themselves c. Retakes are given automatically d. Only the teacher can decide on retakes 9. What constitutes cheating in this classroom? a. Asking for help b. Claiming credit for someone else's work c. Working with a partner d. Participating in study groups 10. What is the penalty for cheating? a. A warning b. A failing grade on the assignment and notification of parents c. Extra assignments d. A detention 11. How will grades be determined? a. By participation only b. By points, with tests and quizzes weighted more than classwork c. By effort d. By attendance 12. Where can students use their cell phones? a. In class anytime b. In the commons and hallways during passing time and lunch c. In the restroom d. In the cafeteria only 13. What happens if a student uses their phone during class? a. They will receive a warning b. The phone will be confiscated immediately c. They can keep it if they ask d. They will lose points on their grade 14. What should a student do if they know they will be absent? a. Ignore it and hope for the best b. Come to the teacher at least three days before c. Ask a friend for notes d. Just show up later 15. If a student is sick and cannot do work, what should they focus on? a. Completing all missed assignments b. Getting better c. Emailing the teacher every hour d. Asking for extra credit 16. What is the policy on bringing food or drinks to class? a. It's not allowed at all b. It’s allowed as long as it’s not a distraction c. Only water is allowed d. Students must share their food 17. How should students contact the teacher with questions? a. Only during class time b. Through social media c. By email or in person d. By sending a friend 18. What happens if a student emails after 9 PM? a. The teacher will respond immediately b. The teacher will respond the next day at 7:45 AM c. The email will be ignored d. The teacher will call the student 19. How do violations accumulate for cell phone use? a. They reset every trimester b. They accumulate throughout the school year c. They reset every week d. They do not count 20. What should students do if they have concerns while the teacher is on maternity leave? a. Contact the principal b. Contact the substitute teacher for assistance c. Wait until the teacher returns d. Handle it on their own Answer Key (Always review AI generated answers for accuracy - Math is more likely to be inaccurate) b. Charged Chromebook, writing utensil, and positive attitude b. A violation card c. Buy a new one for the teacher c. Ask first and only use it during work time b. On Canvas c. It will drop a letter grade each day it is late c. 3 days b. Students must schedule the retake themselves b. Claiming credit for someone else's work b. A failing grade on the assignment and notification of parents b. By points, with tests and quizzes weighted more than classwork b. In the commons and hallways during passing time and lunch b. The phone will be confiscated immediately b. Come to the teacher at least three days before b. Getting better b. It’s allowed as long as it’s not a distraction c. By email or in person b. The teacher will respond the next day at 7:45 AM b. They accumulate throughout the school year b. Contact the substitute teacher for assistance
The Revolt of the Northern Earls (1569) Most people in the North remained loyal to the Catholic noble families who controlled the north and their Catholic faith. When Elizabeth came to power, she promoted ‘new men’ (Protestants) from the gentry and the powerful Catholic nobles lost their power and influence. This led them to organise the most serious rebellion of Elizabeth’s reign in 1569. Why did the Northern Earl’s revolt? The Earls had lost their power when Elizabeth became Queen (and wanted it back). They wanted Catholicism restored in England (and felt that ordinary Catholics would support it). Elizabeth was refusing to marry or to name an heir, causing uncertainty about England’s future. Mary Queen of Scots (if freed from prison) could replace Elizabeth and solve all these problems Who were the key players in the Revolt? Earl of Northumberland • A Catholic who had held an important position under Mary I. • He lost a lot of influence under Elizabeth (as she favoured Protestant gentry) • Elizabeth also took the rights to a valuable copper mine found on his lands Earl of Westmorland • From a rich Catholic family in the north Also the Duke of Norfolk’s brother in law Duke of Norfolk • England’s most senior Protestant noble, but he had very close links to old northern Catholic families, & was sympathetic to them & greedy for power. • He hated William Cecil & Robert Dudley, Earl of Leicester (Elizabeth’s favourite) who were Protestant and from the gentry • He planned to marry Mary QS, but later backed down and urged the earls to call off the rebellion. Mary also supported the plan to marry him What role did religion play? (7/10 – but only because it was linked to power) • Most northerners held onto their Catholic beliefs & although Elizabeth didn’t persecute them, they knew that she wanted their religion to gradually die out, so they supported the revolt. • In 1561 Elizabeth hired a strict Protestant as archbishop of Durham to promote Protestantism in the north, but he was unpopular & turned many northerners against the Protestant religion. What role did politics/power play? (9/10 – this was the most important cause of the revolt) • The Northern Earls lost a lot of their power/influence (even jobs/money under Elizabeth) • Northumberland was jealous of new Protestant families being given top jobs in the North • William Cecil & Robert Dudley were not from ancient noble families, but were very close to the Queen, so the northern Earls resented them getting top jobs in her Government • Elizabeth also confiscated large areas of land & the profits from their copper mines • It is possible, that had Elizabeth allowed the Catholic Northern Earls to keep their jobs, money and influence at court, they may have ‘tolerated’ her as a Protestant Queen (greedy/selfish). What role did Mary Queen of Scots and the Succession play? • Elizabeth was refusing to name an heir and it was becoming clear that she would not marry • If Mary Queen of Scots married the Duke of Norfolk, England would have an heir and England would be Catholic again. The country would be stable without people competing for power. • However, some of Elizabeth’s courtiers got worried that it might not work and that it might lead to charges of treason (punishable by death) • So by September 1569, Robert Dudley (Earl of Leicester) decided to tell Elizabeth about the plot. By this time it was much more serious than simply marrying Norfolk to Mary. • Mary QS had secretly asked Spain to send troops to help the rebellion & overthrow Elizabeth Plan for the Revolt of the Northern Earls (1569) • The Earls of Northumberland & Westmorland will raise rebel troops from their lands in the north and take control of Durham. • The rebels will then march south towards London to join with the Duke of Norfolk • 1000s of Spanish troops will land in England to support the rebel forces • The Duke of Norfolk & rebel forces will seize control of Government & overthrow Elizabeth • Mary Queen of Scots is to be freed, ready to marry the Duke of Norfolk Key Events of the Revolt • Once Elizabeth knew of the plot, Norfolk was arrested and sent to the Tower of London • The Northern Earls were worried they would be executed for their involvement and in a desperate attempt to avoid punishment, pushed ahead with the revolt • They raised an army of ordinary Catholics and took control of Durham cathedral • Catholic mass was celebrated across the north for 2 weeks. • They then headed south, to try and free Mary • Mary QSs was moved south to Coventry on the orders of Elizabeth, so she couldn’t escape • The rebellion failed as Spanish troops never arrived • Elizabeth’s friend (Earl of Sussex) had raised an army of 7,000 men to defend her throne. Results: • The rebellion was a serious threat to Elizabeth • She executed 450 rebels in the north • Northumberland was executed in 1572 & his head was put on a spike on the city gate • The Privy Council called for the Duke of Norfolk’s execution too, but Elizabeth released him. • Mary Queen of Scots was kept in prison for the next 14 years. • The failed plot also led the Pope to take action against Elizabeth • In 1570 he excommunicated Elizabeth from the Catholic Church • He also issued a Papal Bull (order) calling on all loyal Catholics to overthrow her hoping it would encourage another rebellion. • In 1571 Elizabeth called parliament to pass an Act making it treason to claim that she was not the rightful Queen and to bring in/print papal bulls in England. The Significance of the Revolt of the Northern Earls • It was the first and most serious rebellion by English Catholics against Elizabeth • Treason laws were made much harsher • It ended the influence of the powerful Catholic Earls in the North • It led to harsher treatment of Catholics, e.g. 1572 Elizabeth sent the Earl of Huntingdon (strict Protestant) to the north to carry out laws against Catholics (and suppress Catholicism). • Although Elizabeth’s brutal revenge on the rebels show how serious a threat it was, most Catholics in the north stayed loyal, but the Pope’s Papal Bull now put their loyalty in doubt There was little support for the revolt among the rest of the Catholic nobility and ordinary people. When faced with a choice between Elizabeth and their religion, most Catholics chose to support the Queen. 1569, was the last time English Catholics tried to remove Elizabeth by force. The future plots against her were always uncovered by Cecil & Walsingham, before they had a chance to get any public support. Despite this, the Northern Revolt & Papal Bull changed Elizabeth’s attitude towards Catholics who were now seen as potential traitors. From 1570, Elizabeth became less tolerant of recusants (people refusing to attend her church) & took increasingly tough measures against Catholics. The Ridolfi, Throckmorton & Babington plots • In the 1870s-80s, there were 3 Catholic plots to assassinate Elizabeth & replace her with Mary. • The plots were supported by France, Spain, the Pope and some Catholic nobles. • They reinforced the form Mary & from Catholics at home and abroad. Also the threat from Spain. The Ridolfi Plot (1571) • Ridolfi was an Italian banker living in England and a spy for the Pope. • He organised a plot to murder Eliz, marry Mary QS to the Duke of Norfolk & make her Queen. • The Pope & King Philip supported the plot & Philip told the Duke of Alba in the Netherlands to prepare 10,000 troops (but to only invade AFTER the English had overthrown Elizabeth). • The plot failed because Sir William Cecil intercepted coded letters & Norfolk was executed. • Mary was kept under closer watch. • Ridolfi was abroad when the plot was discovered and never returned to England. 1574: Catholic Priests and Priest Holes • From 1574 Catholic priests were smuggled into England to keep the religion alive. • They stayed with rich Catholic families, so Catholic families were kept under surveillance. • Catholic homes were raided – to find ‘priest holes’ where Catholic priests were hiding. • Catholic priests who were found could be hung, drawn and quartered (although not all were) • In 1581, Parliament also passed 2 new tougher laws against Catholics: • Recusants would be fined £20 (which would bankrupt most families) • Trying to convert people to Catholicism was now treason (punishable by death) The Throckmorton Plot (1583) • It aimed to assassinate Elizabeth and replace her with Mary. The French Duke of Guise (Mary’s cousin) would invade England with an army, funded by King Philip (Pope also supported it). • An Englishman, Throckmorton carried messages between Mary & Catholic plotters abroad. • Sir Walsingham (Secretary of State) uncovered the plot after his agents found the plans for the plot in Throckmorton’s house. Throckmorton confessed under torture and was executed. Significance: • The plots showed that Mary’s presence in England posed a serious threat • It also showed that France & Spain were a serious threat (& could invade) • Throckmorton’s papers showed a list of Catholic supporters in England, so the threat from English Catholics was also real • 1,000s of Catholics were imprisoned or kept under surveillance/house arrest • In 1585 another Act was passed to make helping Catholic priests punishable by death. • The Bond of Association was signed by the English nobles & gentry & forced them to promise to execute anyone who tried to overthrow the Queen. Weaknesses of the Plots The plots lacked public support & were uncovered by informers & spies before they had the chance to work King Philip was reluctant to destroy his alliance with Elizabeth (France was still a bigger rival) so is support for the plots was half-hearted, he rarely followed through on his promises to help the plotters or send an army The Babington Plot (1586) In 1586, Walsingham used his spy network to PROVE that Mary supported the Babington plot. His evidence persuaded Elizabeth to put Mary on trial & execute her for treason. • This was a plot to murder Elizabeth and put Mary on the throne • France would invade England with 60,000 men and Spain would also send an army • Babington was passing coded letters between Mary & her supporters in England & Europe. • But all of her letters were being intercepted and read by Walsingham. • Walsingham used his spies to follow every stage of the plot & had the letters decoded • One of Mary’s letters approved plans to murder the Queen and free Mary from prison • They also contained the names of 6 Catholics who planned to kill Elizabeth • They were arrested, hung, drawn and quartered for treason. • Mary had been implicated in plots before, but Elizabeth was always reluctant to execute her • But the proof found by Walsingham finally persuaded her to put Mary on trial • In October 1586, Mary was found guilty & was sentenced to death • But Elizabeth still hesitated, and did not sign the death warrant until February 1587. Significance 1) This plot was very significant because by 1585 England was effectively at war with Spain since Elizabeth had sent her army to help the Dutch Protestants fight the Spanish 2) This meant that Elizabeth’ situation was more dangerous than during previous plots. 3) Elizabeth’s government also became more determined to crush Catholicism 4) 1000s of recusants were arrested & 31 priests were executed 5) Mary’s execution removed the Catholic threat at home 6) English Catholics had no one to rally around, & lost hope of overthrowing Elizabeth 7) But Mary’s death increased the threat of a foreign invasion as England was at war with Spain and King Philip had been preparing an attack on England since 1585 8) Mary’s death made Philip even more determined to invade, Mary had left her claim to the English throne to King Philip upon her death Why was Mary Queen of Scots finally executed? 1 • A new Act in 1585 stated that in the event of Elizabeth’s assassination, Mary could be executed as long as she had been proved guilty & Walsingham had provided hard proof. 2 • Another reason was that by 1587, it was clear that Philip was planning to invade England • There were rumours that Spanish ships had landed in Wales & that Mary had escaped. This convinced Elizabeth that Mary had to be executed if she wanted to keep her throne. Walsingham’s Spy Network: • Walsingham (Secretary of State from 1573) had a network of spies all over England & abroad. He had spies in every English town, some were normal people paid to spy on neighbours. • He also had agents and spies in Spain, France, Germany and Italy • He hired mathematicians to crack written codes and people to open/seal letters secretly • He also pressured captured Catholic priests to spy on others for him in return for a pardon. • He used double agents to infiltrate Catholic networks - to help him discover traitors • But he only used torture against Catholic priests caught in England in the most serious cases • But 130 priests and 60 of their supporters were still executed during Elizabeth’s reign. Why did Relations with Spain get worse (1569-1588) • England had tried to stay on good terms with Spain, because Eliz wanted to avoid an expensive war that could lead to her being overthrown (English Catholics could support it) • But by the 1570s, Elizabeth wanted to have an empire of her own. • She also needed to make more money to defend her country and throne (by improving trade) • This religious, political and economic rivalry led to growing tensions between England & Spain Political and Religious Rivalry 1) Land abroad, gave countries wealth/power. By the 1580s, Eliz wanted an empire to rival Spain’s (especially as Spain had supported the Catholic plots against Eliz – even if it was half-hearted) 2) Religion was another cause of conflict. Philip opposed Elizabeth’s religious settlement 1559 3) Luckily for Elizabeth, in the 1550s Spain & France were competing to be the greatest European power and both wanted England as an ally against the other. 4) But from 1567, Spanish ships were sailing to the Netherlands with money for the Alba’s army 5) This alarmed English Protestants and Elizabeth’s Privy Council who put more and more pressure on her to send an army to help the Dutch Protestant rebels (in the Netherlands). Economic (commercial) Rivalry: The New World, privateers and Sir Francis Drake • Under Elizabeth, English merchants wanted to make big profits in the New World (Americas). • However, trading in the New World was difficult because of Spain’s power 1) Spain controlled most of the New World where there were huge profits to be made and anyone who wanted to trade there needed a licence from Spain (which it would not give): 2) But the Americas had valuable crops like tobacco, sugar, and also silver and gold 3) Elizabeth secretly encouraged privateers to trade illegally & raid Spanish ports & ships 4) At first Elizabeth denied responsibility for their actions, which delaye war with Spain Sir Francis Drake: Elizabeth sends Drake to rob Spanish colonies and ships (which infuriates Spain) 1) Spain’s support for the Ridolfi plot (1571) made her more willing to support Drake • In 1572 Eliz hired Drake to sail to the New World & steal £40,000 of Spanish silver • In 1577 she sent Drake back again with a secret mission to rob Spain’s colonies/ships • Drake brought back £400,000 of Spanish treasure & claimed an area of California in Elizabeth’s name (New Albion). He gave a lot of this money to Elizabeth • He boosted England’s finances at a time of growing concern over Spain’s threat • He became famous as the first Englishman to circumnavigate the globe. • Eliz knighted Drake as a reward, which infuriated Philip (as he saw Drake as a pirate) • Drake’s actions & his claim to California made it clear that England did not accept Spain’s domination of the New World. Elizabeth’s Support for the Dutch Rebels led to War with Spain (1585-88) • By the 1580s, tension between England & Spain had reached boiling point • At first, Eliz refused to send her army to help the Dutch rebels, because she wanted to avoid a war with Spain. So she tried to get the Spanish to leave the Netherlands in other INDIRECT ways: 1) By allowing Drake (& other English privateers) to attack and rob Spanish ships and colonies 2) By encouraging others (the French heir/mercenaries) to fight the Spanish in the Netherlands • In the 1570s, Elizabeth promised to marry the heir to the French throne (the Duke of Alencon) so that he would take an army to fight the Spanish in the Netherlands The Spanish Fury (1576) and the Pacification of Ghent (1576) • By 1576, the Spanish Govt in the Netherlands was bankrupt (the war was expensive) • After months without pay, Spain’s soldiers violently robbed Dutch towns in the “Spanish Fury” Spanish troops rebelling and robbing cities in the Netherlands in 1576. This united the Dutch Protestants & Catholics against Spain. They drew up the ‘Pacification of Ghent’ (demanding that): • Spanish troops leave the Netherlands • Spain allows the Dutch to rule themselves • The persecution of Dutch Protestants stops What did Elizabeth do? • Elizabeth sent £100,000 to help the Dutch rebels • In 1577 King Philip’s brother, Don Juan agreed to the rebels demands (but this was a trick) as just 6 months later Philip sent an even bigger army to attack the Dutch. • Elizabeth then hired a mercenary army of 6000 English & Scottish volunteers to help the Dutch. • But her plan backfired because the mercenaries destroyed Dutch Catholic churches, which caused the Catholics to make peace with Spain. • In 1578, her Privy Council urged Eliz to send her official army to help the Dutch, but she refused. The Dutch were disappointed & turned to France for help. The French Duke of Alencon arrived with an army to fight the Spanish, but by 1579 Spain had taken control again. • In 1580 Spain got even stronger after Philip won control of Portugal & its empire. • So Elizabeth gave the Duke of Alencon £70,000 to help him fight the Spanish • In 1582, Alencon took his army the Netherlands but failed to defeat Spain. • Elizabeth’s foreign policy in the Netherlands had failed & she had only managed to annoy Spain 1585: Why did Eliz finally decide to send her army to the Netherlands? (she lost her 2 main allies) • 1584 the Duke of Alencon died (so he could no longer fight the Spanish in the Netherlands) • 1 month later, William of Orange, the leader of the Dutch Protestant rebels was assassinated. • In 1585, Spain signed the Treaty of Joinville with France, agreeing to stamp out Protestantism in France/Europe meaning France & Spain were now allies against Protestantism • Elizabeth now felt she had no choice but to send her official army to the Netherlands • She signed the Treaty of Nonsuch with the Dutch rebels which promised them military help 1585: Robert Dudley’s campaign in the Netherlands was unsuccessful She sent 7,400 man army to the Netherlands led by Dudley. But he accepted the title of ‘Governor General’. Eliz was angry as it suggested that she had deposed King Philip so she told Dudley to resign this position. His army was defeated by the bigger Spanish Army as Eliz had not provided him with enough money to win. In 1587 Dudley resigned and returned to England. At the same time, Eliz had sent Drake to raid Spanish colonies in the New World to disrupt King Philip’s flow of money. Philip was furious and told the Pope he planned to invade England at the end of 1585. Drake singes the King of Spain’s beard 1587 • In 1587 Elizabeth ordered Drake to attack Spain’s most important port Cadiz • He destroyed 30 ships in 3 days – known as the ‘Singeing of the King of Spain’s Beard’ • He also stole lots of wood, meaning the Armada did not have quality barrels for food/water • Drake’s disruption delayed the Armada by a year (& meant that its food rotted in 1588). • This bought England more time to prepare for war. The Spanish Armada (1588) The Plan • By 1588, the Spanish Armada was ready to invade England • It had 130 ships with 8000 sailors & 18,000 soldiers • The Duke of Medina Sidonia would lead the Armada, but he had little experience at sea and didn’t want the job • The Armada would collect Parma’s army from France & sail to England under the protection of the Armada’s warships • Parma would march to London to depose Elizabeth & impose a Catholic government in England. 1) The Armada reached the English Channel The Armada set out in May 1588, but was delayed for a few weeks by bad weather In July the Armada was near England & signal fires were lit to warn Elizabeth English ships set sail to meet the Armada The Armada sailed up the channel in a crescent (half moon) formation, to use the large armed galleons to protect the weaker supply and army ships The English navy carried out a few minor raids, but did not inflict much damage Only 2 Spanish ships were lost (by accident) 2) The English attack the Spanish at Calais (with fire ships) and at Gravelines The Armada sailed up the English channel & anchored at Calais to wait for Parma’s army But Parma’s men didn't reach the coast in time (news had reached them too late) At midnight, the English sent 8 fireships into the Spanish ships causing panic They cut their anchors, broke formation & headed for the open sea (without Parma) The Spanish ships sailed to Gravelines, but bad weather stopped them returning to Calais The English attacked and the battle lasted many hours (5 Spanish ships were sunk) The rest were forced to sail away from France towards Scotland The English ships followed them to make sure they didn’t come back to collect Parma’s army 3) The Armada’s Journey back to Spain around Ireland was a disaster The Spanish called off the attack and returned to Spain around Scotland & Ireland Bad storms sank many ships and wrecked more on the Irish coast Many sailors died from starvation & disease – less than half the men made it back to Spain How did England defeat the Spanish Armada? !) Faster Ships • Years before the battle, England had started building smaller, faster ships (galleons) that could fire canon balls quicker & further than Spanish ships • Spanish ships were huge and slow to change direction. 2) Bad Planning & Communication (Spanish) • Philip’s plan to join with the Duke of Parma’s army in France was risky. • Parma had lots of small ships which took 48 hours to load, man and set sail. • It took too long (a week) for word to reach Parma that Medina was in the English Channel, by which time Medina had set sail to Calais. • Parma was not ready to set sail & the English were already ready to attack (leaving Medina with very little back up when anchored in France). 2) English Tactics were more effective • Spanish ships aimed to come alongside the English ones, jump on board & fight the enemy. But the English ships were faster & kept a safe distance. • They chased the Armada down the Channel, with heavy cannon fire, which forced the Spanish to arrive in France before Parma’s army was ready • As the Armada was waiting, the English sent fireships into the Spanish fleet. • This caused the Armada to panic, cut their anchors & sail away to the north • When the Spanish ships regrouped, the English attacked them in the Battle of Gravelines & the Armada was forced to sail north, chased by faster ships. 5) Bad Weather • Strong winds made it impossible for the Armada to return & pick up Parma’s army and storms wrecked or sunk Spanish ships as they tried to return home along the Scottish-Irish coasts. 2) Spanish Supplies • The Armada was not well supplied with food/weapons. Drake’s attack on Cadiz port in 1587 had destroyed food barrels. Delays in setting sail meant that by the time the English attacked the Armada it had been at sea for 10 weeks and had rotting food. 1000s died from starvation/disease. The consequences of the English victory? • Victory over the Spanish Armada gave Elizabeth a great propaganda victory • A new portrait was made, and a medal was made to commemorate her victory, it said “God blew and they were scattered”. • Elizabeth claimed that God was on the side of Protestantism • This led to a feeling of English pride and encouraged the Dutch rebels to renew their fight against the Spanish • The defeat of the Armada showed the strength of the English navy and gave England the confidence to trade and explore more widely at sea • Although Philip did not give up and continued the war for the rest of Elizabeth’s reign, the defeat had cost Spain dearly, both financially and in terms of its power • The Armada marked the start of a long decline in Spain’s power and fortunes. • English ships were sent on voyages of discovery and set up valuable new trade routes • By the end of Elizabeth’s reign, the navy was also trying to set up a new colony in Virginia • The English victory boosted Elizabeth’s popularity & strengthened the Protestant cause
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.