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Is that a car, Grandpa? No, it’s a tractor. You can drive it on the farm. What is a farm? A farm is where you grow food and raise animals. Are you a farmer, Grandpa? No, but my father was a farmer. He worked on a farm. Oh, I see. Do you like farms? Yes, I do. Farms have many animals.
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A trip to Rio Julia and her family traveled from New York to visit Rio de Janeiro in Brazil. Julia's cousin Gabriela lived there. They all went to the opening night of the Olympics. The stadium was very crowded. It made Julia nervous. Everyone screamed and cheered. Their seats were far away. Julia could barely see. The music was loud. It made her head hurt. Julia had been happy to visit Rio. Now she just wanted to go home. Gabriela woke Julia up the next morning. "There's another Olympic event today!" she said. Julia did not want to go, but she smiled and got ready. The families walked through shady streets. Gabriela's street ended at a beach. Julia stopped and stared. Tall buildings stood along the beach. Olympic racing boats floated on the water. There was a big mountain behind them. "That's Sugarloaf Mountain," Gabriela said. It was beautiful. The next day, Julia ran to Gabriela's room. "We're going up Sugarloaf Mountain!" she said. They rode a cable car. It hung high above the city. Julia stared out the window. White buildings stood above the green jungle. They went to a big market. Julia tasted a mango. It was not like the mangoes at home. It was juicy and sweet! They went to an Olympic swimming race. Gabriela's brother, Chaz, cheered, "Go Brazil!" "Brazil is not even in this event!" Gabriela said. "Oh." Chaz said. He smiled at Julia. "Go Americа!" It was Julia's last day in Rio. They went to Grandma and Grandpa's. Julia remembered the house. She had visited when she was five. Grandpa had taught her to dance. It felt like home. Grandma made a spicy bean stew. After lunch, they went to an Olympic football game. "The crowd is very noisy," Julia said. "I'm scared." "Don't worry," Grandpa said. "Football fans are one big family." At the stadium, the crowd seemed even louder. Julia held Grandpa's hand. Brazil got the ball. Everyone cheered. Julia got caught up in the game. She cheered, too. Then, Brazil scored a goal. The crowd cheered. Grandpa lifted Julia in the air. They sang a song with the crowd to celebrate.
What Is a Tornado? The sky is dark far away. Something moves down from the clouds. It spins across the land. It sounds like a very loud train. A tornado is coming! A tornado is a spinning cloud. It is shaped like a funnel. Its winds can reach 300 miles per hour. That is faster than a race car. The spinning air pulls things up. It can toss a car in the air. It can even destroy, or ruin a house. A tornado can be dangerous. It can cause harm to people and places. How Does a Tornado Form? A tornado is a kind of weather. Weather is the condition of the air. Most tornadoes begin as a kind of weather called a thunderstorm. Thunderstorms are harsh rainstorms with thunder and lightning. These rough storms have high winds and heavy rain. When high winds spin and touch the ground, a tornado is born. Most tornadoes do not stay on the ground for long. When they do, they can cause a lot of damage, or harm. A tornado is a big event! Where Do Most Tornadoes Happen? More tornadoes happen in the United States than anywhere in the world. Most of them form in the middle part of our country. Scientists think this might be because warm, wet air from the Gulf of Mexico crashes with the cool, dry air from Canada. This area is known as Tornado Alley. How do Tornadoes Affect People? Tornadoes affect people and towns in many ways. Weak tornadoes break branches from trees or damage signs. Strong tornadoes can destroy buildings. People who live in areas where there are many tornadoes always think about the weather. They listen to the radio and watch news reports on television. Schools provide tornado drills so children can practice being safe in the event of a tornado. Teams of people work together to repair the damage caused by a tornado. How Can You Stay Safe? There are ways to prevent, or stop harm during a tornado. News reports use the words tornado warning to give notice that a tornado has been seen. Following safety rules can help everyone stay safe during a tornado!
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.
1.Linguistics is the science that studies language. 2.Linguist:Someone who studies linguistics. 3.The Subfields of Linguistics Phonetics deals with the sounds of language. Phonology deals with how the sounds are organized. Morphology deals with how sounds are put together to form words. Syntax deals with how sentences are formed. Semantics deals with the meaning of words, sentences, and texts. Pragmatics deals with how sentences and texts are used in the world (i.e., in context) Text Linguistics deals with units larger than sentences, such as paragraphs and texts. 4.Prescriptive: This approach consists basically of stating what is considered right and wrong in language. 5.Descriptive: This approach, on the other hand, consists of describing the facts. Descriptive linguistics is dedicated to describing the rules of the language, and the language is seen as essentially rule governed. 6.Language is rule-governed, creative, universal, innate, and learned, all at the same time. 7.Linguists understand language as a system of arbitrary vocal signs. 8.Linguistic signs: involve sequences of sounds which represent concrete objects and events as well as abstractions.Signs may be related to the things they represent in a number of ways. 9.Iconic: which resemble the things they represent (as do, for example, photographs, diagrams, star charts, or chemical models). 10.Indexical: which point to or have a necessary connection with the things they represent (as do, for example, smoke to fire, a weathercock to the direction of the wind, a symptom to an illness, a smile to happiness, or a frown to anger). 11.Describe the characteristics of human language: Creative: (The structural elements of human language can be combined to produce new utterances, which neither the speaker nor his hearers may ever have made or heard before.) Rule-governed: (Language is made of rules.) Universal: (There are some aspects that are present in all languages of the world.) Innate:(all humans possess an innate capacity for language, activated in infancy by minimal environmental stimuli. Chomsky) Uniquely human: (Language is what sets us apart from other species. It is what makes us human.) Learned:(Children acquire language from their natural setting.) 12.Differentiate between iconic, indexical and symbolic signs. A. iconic, which resemble the things they represent (as do, for example, photographs, diagrams, star charts, or chemical models) B. indexical, which point to or have a necessary connection with the things they represent (as do, for example, smoke to fire, a weathercock to the direction of the wind, a symptom to an illness, a smile to happiness, or a frown to anger). c. symbolic, which are only conventionally related to the thing they represent (as do, for example, a flag to a nation, a rose to love, a wedding ring to marriage). 12. Distinguish between different senses of the grammar word. The prescriptivist´s grammar (Grammar is a set of rules that label the different utterances as either right or wrong.) The descriptivist´s grammar (Grammar is a set of rules that govern the langauge spoken by people. ) The linguist´s grammar (Grammar is the subconscious knowledge of the set of rules that enables speakers to use the language) The speaker´s grammar (Grammar is the intrinsic linguistic knowledge within a native speaker) 13.Describe common fallacies about language and grammar: ►One type of grammar is simpler than another. ►Changes in grammar involve deterioration in a language ►Grammars should be logical and analogical (that is, regular) ►People must be taught the grammatical rules of their language. ►Only some languages have grammar. ►Grammars differ from each other in unpredictable ways. 14.Generality: All Languages Have a Grammar 15. Equality: All Grammars Are Equal 16.Changeability: Grammars Change Over Time 17. Universality: Grammars Are Alike in Basic Ways 18.Tacitness: Grammatical Knowledge Is Subconscious 19.Linguistics is defined as the study of language systems. It is the scientific study of language. 20.Historical approach:It is the study of language change. 21.Linguistic Competence: is the unconscious knowledge speakers of a language have about the system that enables them to create and understand novel utterances. 22.Performance: is the use of it. Performance is “the actual use of language in concrete situations.” 23.I-Language (internal language): which is the intrinsic linguistic knowledge within a native speaker. 24.E-Language (external language): which is the observable language—the output from a speaker. 25.Parole ('speech') refers to the concrete instances of the use of langue, including texts which provide the ordinary research material for linguistics. 26.Langue: 27.Language: is a system of communication that is non-stereotyped and non-finite; it is unlimited in its scope. 28.Grammar: to refer to a subconscious linguistic system of a particular type. Grammar makes possible the production and comprehension of a potentially unlimited number of utterances. 29.Communication and animals: Selecting a mode of communication (speech,writing, gesture). Delivering the symbols through a medium, a physical basis for communication, light, air, or ink. Decoding of the symbols to obtain the information. 30.SIGNS: Communication relies on using something to stand for something else. Words are an obvious example of this: You do not have to have a car, a sandwich, or your cousin present in order to talk about them—the words car, sandwich, and cousin stand for them instead. This same phenomenon is found in animal communication as well. 31.The signifier: A signifier is that part of a sign that stimulates at least one sense organ of the receiver of a message.A signifier can also be a picture, a photograph, a sign language gesture, or one of the many other words for tree in different languages. 32.The signified: The signified component of the sign refers to both the real world object it represents and its conceptual content. The first of these is the real world content of the sign, its extension or referent within a system of signs such as English, avian communication, or sign language. 33.Iconic signs or icons: always bear some resemblance to their referent. A photograph is an iconic sign; so too is a stylized silhouette of a female or a male on a restroom door. 34.Some iconic tokens: a. open-mouth threat by a Japanese macaque; b. park recreation signs; c. onomatopoeic words in English. 35.An indexical sign, or index, fulfils its function by pointing out its referent, typically by being a partial or representative sample of it. Indexes are not arbitrary, since their presence has in some sense been caused by their referent. For this reason it is sometimes said that there is a causal link between an indexical sign and its referent.The track of an animal, for example, points to the existence of the animal by representing a part of it. The presence of smoke is an index of fire. 36.Symbolic signs: bear an arbitrary relationship to their referents and in this way are distinct from both icons and indexes. Human language is highly symbolic in that the vast majority of its signs bear no inherent resemblance or causal connection to their referents, as the following words show. 37.Mixed signs Signs: are not always exclusively of one type or another. Symptomatic signs, for example, may have iconic properties, as when a dog opens its mouth in a threat to bite. Symbolic signs such as traffic lights are symptomatic in that they reflect the internal state of the mechanism that causes them to change color. 38.Signals: All signs can act as signals when they trigger a specific action on the part of the receiver, as do traffic lights, words in human language such as the race starter's "Go!", or the warning calls of birds. 39.SIGN STRUCTURE: No matter what their type, signs show different kinds of structure. A basic distinction is made between graded and discrete sign structure. 40.Graded signs convey their meaning by changes in degree. A good example of a gradation in communication is voice volume. The more you want to be heard, the louder you speak along an increasing scale of loudness. There are no steps or jumps from one level to the next that can be associated with a specific change in meaning. 41.Discrete signs are distinguished from each other by categorical (stepwise) differences. There is no gradual transition from one sign to the next. The words of human language are good examples of discrete signs. 42.A VIEW OF ANIMAL COMMUNICATION ►Largely iconic ►Largely symptomatic ►Little arbitrary ►Not deliberate ►Not conscious ►Not symbolic ►Stimulus bound
To understand melody in music, think about some music you’re familiar with. If you were asked to hum it, what would that sound like? The part of the music that you’d hum is the melody. It’s the main thread of sound that your brain tracks and holds onto when you’re listening to music. In vocal music, the melody is sung by the lead singer. Other vocalists can provide harmony and instruments can add accompaniment, but the melody is the star of the show.What are the characteristics of melody in music? How do you describe a melody in music? A melody needs to have two things. The first is a sequence of notes, or pitches, which range from high to low. The second is rhythm, which is the timing and duration of each note. These two simple elements can create an incredible variety of combinations. Even though a melody only consists of one note at a time, it can convey so much energy and emotion. Melodies can be fast and sparkly, like “The Flight of the Bumblebee.” They can be slow and majestic, like “Finlandia.” They might be sweeping and graceful, like a Strauss waltz. Or they can be fun and exciting, like your favorite pop tunes that you love to sing along with. Melodies often tell you a lot about where a piece of music comes from. It’s easy to recognize and identify melodies from different folk traditions such as the Japanese folk song “Sakura” or the Irish tune “Star of the County Down.” Learn how to play your favorite melodies on piano, and more! Sign up now. What is melody in music? Here are some examples. Here is the famous melody for the song “Lean on Me” written out on a staff. Notice the way that the notes move up, down, and then repeat. What is melody in music? Example of Lean On Me notes on treble staff. A melody all by itself is great, but music can be even more fun when there’s an accompaniment. Here are a few bars of “Lean on Me” with the accompaniment written out. As you listen to this song, notice how the accompaniment has a very similar rhythm and movement to the melody. Then there’s that one note in the bass line that comes along every measure with its own rhythm, which adds some extra energy and movement to the song. What makes a good melody? When you create a melody, there are four types of movement you can use: Repeat (same note) Step (up or down) Skip (up or down) Leap (up or down) Stepping and repeating are the most common types of melodic motion, and this makes a melody easier to sing. Most “hummable” tunes use steps and repeats almost exclusively. This kind of melody is called conjunct. Beethoven’s “Ode to Joy,” one of the most famous melodies of all time.Skips and leaps are generally more sparing in melodies, but when thoughtfully placed they can have a powerful emotional impact. Tunes with a lot of leaps are called disjunct. Listen to Sarah Brightman sing All I Ask of You from The Phantom of the Opera starting at 0:39. This is a very disjunct melody, and challenging to sing. Great melodies also incorporate patterns that blend unity, repetition, and contrast. Our ears love patterns, but they also love novelty and growth. A good melody incorporates all of these elements. For example, listen to John William’s “Princess Leia Theme.” Can you hear the repeated pattern in the melody that gradually moves higher as the theme progresses? Now listen to the way it changes and develops into something that fits with what came before but sounds new at the same time. This is some great melodic writing! Can melody exist without rhythm? There is no way for a melody to exist without rhythm. Even if your melody only has one note, that note has a duration, and that’s the rhythm. If your melody has two notes, how long those notes last and how much time passes between hearing them is also a rhythm. A melody in music can often be recognized even when it’s performed with different rhythms. This frequently happens in live performances of pop, rock, and jazz, in which singers typically improvise slight rhythmic differences with each performance. No two renditions are exactly the same, and this constant reinterpretation keeps the music fresh. How to make a melody for a song on piano Creating your own melodies on the piano is easy and fun! There are so many ways you can discover a melody all your own. Here are a few ideas. Get some inspiration from the world around you. What can you hear right now? A clock ticking? A bird song? A car passing by your house? See if you can find some notes on the piano that imitate the sounds you hear. Think of a feeling you’d like to put into a melody. What are some ways you could make a string of notes sound happy, sad, angry, or maybe just thoughtful. Choose a line from a poem you like, or write your own. Read it out loud and put some feeling into it. Did your voice rise and fall in pitch as you were reading? Now go to the piano, start on any note you like, and try to imitate what happened when you read. Go up when your voice naturally went up, go down when your voice naturally went down. How did that sound? Now you have the perfect melody to go with those words. Too many keys on the piano? The truth is, most melodies use only a limited number of different notes. Try creating a melody using only the black keys. These form what’s called a pentatonic scale. It’s used in a lot of folk music traditions around the world and can be a great place to start if you want to create your own melodies. Remember, when you create your melody, keep it simple. Use repeated notes and steps, but add a few skips to keep things interesting. One tip about leaps: when you do put in a big leap, try doubling back and filling in the empty space you leaped over. This keeps the melody self-contained and easier to sing. Also, see if you can use the same patterns of notes and rhythms to give the melody unity, but also change those patterns to give it variety. There is no right or wrong way to create your own music. Keep trying combinations of notes and rhythms until you find something that you like. How many bars and notes are in a melody? Many types of music tend to have a prescribed number of bars, or measures. This will vary widely between different genres, and creates an overall sense of musical structure. If you’re writing a pop song, a verse will usually have between eight and sixteen bars. The prechorus that follows often has just four bars, and this “foreshortening” creates a sense of acceleration, driving the listener toward the chorus. The number of notes can also vary widely. A melody in music needs at least two notes, and a long and complex one can have hundreds or even thousands of notes. What is a countermelody in music? How many melodies should a song have? A counter melody is a melodic line that interacts with the primary melody as an independent but supportive voice. A great example of this is the song “We Don’t Talk about Bruno.” Each character sings their own melody during the piece, but these melodies all combine at the end as countermelodies. This produces a musical texture known as counterpoint. The same thing happens in “One Day More” from Les Miserables. The different melodies are first sung separately, but end up being combined in a splendid, complex texture that leads the music to its thrilling conclusion. The difference between a countermelody and regular harmony is that harmony usually supports the rhythms of the melody. A countermelody will move more independently, with different rhythms from those of the melody, and will often sound “melodic” when sung or played all by itself. A melodic song should have one main melody. This is the part that the lead voice sings. It’s usually in the spotlight, and will be the most memorable part of the music. Anything else is either harmony, countermelody, or accompaniment. Does all music have to have a melody? A piece of music doesn’t have to have a melody. There are many different kinds of music without melody. For example, a lot of music played on percussion instruments won’t have a melody. Listen to this example of Tahitian drumming. This is some great music, exciting and fun to listen to, but you’d have a hard time humming it. It’s music, but it doesn’t have a melody. Rap music is another style of music where there doesn’t have to be a melody. In rap, words are chanted rather than sung. The performer will raise and lower the pitch of their voice for emphasis, but it’s the rhythm of the words that creates most of the music. Music can even lack any melody, at least in some sections. Listen to the opening chords of “Duel of the Fates.” This choral passage is all about harmony, with little rhythmic variance or sense of melody. But it makes an effective contrast with the next section, which is bustling with rapid instrumental melodies. In some pieces, there are multiple melodic lines but there is no one main melody. When music is made up of equally important countermelodies, it creates a contrapuntal texture. Baroque composer J.S. Bach was one of the greatest masters of this style, such as in his Little Fugue in G minor. It starts with a single melodic line, the subject, but then a countermelody is added, and then more and more until several melodic lines are playing together. It’s fun to listen to, but once all the countermelodies are playing together it becomes hard to decide which part to hum along with! You’ll also hear a lot of counterpoint in jazz music, in which the different instruments are all playing together and improvising their own melodies that combine to create a rich, thick musical texture. Experience the wonder of melody in music! Whether you’re humming your favorite tune, or creating a new song all your own, melody is a memorable, shareable part of music. Enrich your music experience by being aware of, listening for, and enjoying the melodies all around you.
Tornadoes Introduction. What can lift roofs from buildings and sweep houses into the air? Tornadoes can! Tornadoes come in many sizes. Some tornadoes are only a few feet (1 meter) across. Others are more than a mile (1.6 km) wide. Some tornadoes touch down for a short time. Others travel for hundreds of miles. How Tornadoes Form. Why do tornadoes happen? Scientists are not sure. Tornadoes come from giant thunderstorms called supercells. A supercell happens when warm, moist air rises to mix with cold, dry air. The mixing of cold and warm air causes the air to spin. The spinning wind turns into a cloud in a funnel shape. As the cloud turns, the wind becomes stronger. When the funnel cloud touches the ground, it is a tornado. Measuring Tornadoes. Scientists have a way to measure the strength of tornadoes. They look at the harm caused by a tornado. They use the amount of harm to estimate the wind speed. They use a special scale called the EF Scale. The EF Scale measures the strength of the tornado. Where Tornadoes Form. Tornadoes may be hard to measure, but scientists have a good idea where they'll strike. It's true that a tornado can hit anywhere in the world at any time. Most tornadoes happen in the central part of the United States. This area is called Tornado Alley. More than one thousand tornadoes strike Tornado Alley each year. Tornado Safety. There is no way to be sure that a tornado will strike. The National Weather Service (NWS) tries to help people stay safe during tornadoes. If they put out a tornado watch, a tornado might strike. If they put out a tornado warning, a tornado has been spotted. If there is a tornado warning. it's important to get to a safe place. Go indoors. The safest place is a basement. If you can't get to a basement, go into а closet or bathroom. The spinning air in a tornado makes things fly around. This can be dangerous. It's always important to protect your head. You should get close to the ground. Go under a desk or table. You can even lie down in a bathtub. It is not safe to stay in a mobile home in a tornado. If you are in a tall building, go to the stairs. If you are in a car, wear your seatbelt and lean forward. If you are outside, lie down on the ground. Conclusion. Tornadoes are amazing and scary examples of the power of nature. People still have many questions about tornadoes. What causes a tornado? What is it really like inside a tornado? Maybe we will find out one day.
Taxi! Captain Ben Fawcett has bought an unusual taxi and has begun a new service. The 'taxi' is a small Swiss aeroplane called a 'Pilatus Porter'. This wonderful plane can carry seven passengers. The most surprising thing about it, however, is that it can land anywhere: on snow, water, or even on a ploughed field. Captain Fawcett's first passenger was a doctor who flew from Birmingham to a lonely village in the Welsh mountains. Since then, Captain Fawcett has flown passengers to many unusual places. Once he landed on the roof of a block of flats and on another occasion, he landed in a deserted car park. Captain Fawcett has just refused a strange request from a businessman. The man wanted to fly to Rockall, a lonely island in the Atlantic Ocean, but Captain Fawcett did not take him because the trip was too dangerous.
Growing up in Sioux Falls, South Dakota, a small city surrounded by endless plains, I've found unexpected echoes of home in China's smaller towns — from the warmth of locals in Huaihua, Central China's Hunan province, to the quiet charm of Yangshuo, South China's Guangxi Zhuang autonomous region. With an itch to see more of China's lesser-visited regions, I began planning a trip to the northwest with seven friends — five Americans, one Pakistani, one Zimbabwean, and one Colombian. We bought round-trip tickets from Shanghai to Yinchuan, Ningxia Hui autonomous region, for less than $120 each. From there, we planned to rent a car and drive to Xining in Qinghai, then on to Qinghai Lake, and finally to Lanzhou, Gansu. To make that possible, several of us applied for Chinese driver's licenses, a process that involved translating our US licenses into Mandarin and passing a short test on traffic laws. Within a day, we were licensed. As we piled into two rental cars in late March to begin our eight-day journey, it became clear that this wasn't just a road trip — it was the culmination of our four years in China, the Mandarin we had so diligently studied, and our ongoing effort to contribute to US-China people-to-people relations. Right away, we drew curious reactions. At the Yinchuan airport, taxi drivers offered us rides into the city, only to stare in astonishment when we told them we had rented cars. "You're driving? In China?" one driver asked, visibly surprised. It was a reaction we'd encountered multiple times during our trip, as foreign drivers are rare in China, especially in remote regions. In Yinchuan, we stocked up on snacks and adjusted to the chilly desert air. From there, we headed west, navigating wide highways framed by dramatic landscapes: arid plains, jagged mountains, and occasionally, a herd of sheep crossing the road. The vastness of the Northwest was humbling — and as someone who grew up on the wide-open prairies of South Dakota, it felt oddly familiar. One of the highlights of our trip was camping by Qinghai Lake, the largest saltwater lake in China. A few summers ago, Santiago Solano, one of my classmates from the US, cycled from Xi'an in Shaanxi to Urumqi in the Xinjiang Uygur autonomous region over the course of a month and met many kind strangers along the way. One of them was Geng San, a Tibetan lamb herder who managed a piece of land right next to Qinghai Lake and graciously invited us to camp there. "That's what China is — it's the people. The quiet generosity of an old Tibetan nomad who, years after we first met, still offered us a place to rest on his land," said Solano, who is also part of the group on this trip. But apparently, we underestimated just how cold it would be to camp next to Qinghai Lake in late March. It was deathly freezing. In preparation for the trip, we had ordered two tent kits and eight sleeping bags. However, when the temperature eventually dropped to — 10 C, all of us piled into the cars and turned the heaters on. So much for camping. From Qinghai Lake, we drove to Lanzhou, where we visited many food markets and tried every type of noodle on offer. Since we are college students, we rented a gaming hotel room — something I've only ever seen in China. At night, instead of attending local parties as we had before, we stayed in the hotel and gamed late into the morning. For me, the trip was as much about the journey as it was about the destinations. Driving through Northwest China gave us a unique perspective on the region's natural beauty and its people. At gas stations, shopkeepers greeted us with curiosity and kindness, often offering recommendations for nearby attractions. At roadside carts, we sampled local specialties, grabbing a quick skewer and a mango for the road. And at every stop, we were touched by the warmth and hospitality that make traveling in China so rewarding. As an American who has lived in China for several years, I'm often asked about my experiences here. Trips like this one remind me of the similarities between the two countries, despite their differences. Just as road trips are a quintessential part of American culture, they've become my favorite way to explore China. Whether it's driving through the rolling hills of South Dakota or the deserts of Ningxia, there's something universal about the freedom and camaraderie that come with having complete control over where you end up. Written by Charlie Howes, a 22-year-old American who has lived in China since 2019. He completed his final year of high school at Beijing No 80 High School and is currently studying at New York University Shanghai. He has founded a company in China focused on facilitating US-China trade and plans to continue living in Shanghai long term. He enjoys road trips, cycling around the world, learning languages, and meeting new people.