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6-3 Practice
Quiz by Adriana Villegas
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Algebra 2 6.3.4 Practice
3 6 practice
Section 6.3: Exponential Functions Practice
Grammar Practice 3: Unit 6
Multiplication Practice 3's-6's
In a single domesticated grain seed, one might see the bud of great civilizations. The birth of agriculture was a turning point in humans' social development, as stable food supplies enabled people to transcend the constraints of food gained by hunting and gathering. After that, people were able to settle down and experience population booms. As one of the major areas around the globe where agriculture originated, China has contributed to the world's domesticated rice, millet, buckwheat and soybeans. Archaeological studies have unveiled that the planting of rice originated around 10,000 years ago in the lower reaches of the Yangtze River, leading to the eventual replacement there of hunting and gathering practices dating back 5,000 to 6,000 years. "It marked the formation of a rice-based agricultural society in the area," said Zhao Zhijun, an archaeologist at the Chinese Academy of Social Sciences. Archaeological studies of the origins of rice-based agriculture are an important part of a national project tracing the origins of Chinese civilization itself. President Xi Jinping has greatly valued the project. At a group study session of the Political Bureau of the Communist Party of China Central Committee on May 27, 2022, Xi, who is also general secretary of the CPC Central Committee, emphasized the significance of the project and the role that archaeological studies play in better understanding Chinese civilization. The project to trace the origins of Chinese civilization, in addition to finding signs of human activity more than 1 million years ago, has also proved that China's history includes 10,000 years of culture and more than 5,000 years of civilization. The project has provided clear knowledge of the origins and formation of Chinese civilization, the history of its development, the process of the formation and development of its pluralistic and integrated pattern, and the characteristics of the civilization and why it was formed in such a way, he added. This was not the first time that Xi emphasized the importance of the origin-tracing project. Since the 18th National Congress of the CPC in 2012, Xi has toured more than 100 historical and cultural locations and issued many instructions related to archaeology and the origin-tracing project. During the 23rd group study session of the Political Bureau of the CPC Central Committee in 2020, Xi called for giving more attention to archaeological research and letting historical facts speak for themselves. "This will provide strong support for our efforts to carry forward the best of traditional Chinese culture and increase our cultural confidence," said Xi. The origin-tracing project has been carried out since 2002. Its ongoing fifth phase, which started in 2020, involves the participation of more than 500 researchers from 29 institutes across the country. It primarily centers on several ancient capital sites, including the Liangzhu site in Hangzhou, Zhejiang province, the Taosi site in Xiangfen county, Shanxi province, the Shimao site in Shenmu, Shaanxi province, and the Erlitou site in Luoyang, Henan province, from 3,500 to 5,500 years ago, as well as other settlements mainly along the basins of the Yellow, Yangtze and Liaohe rivers. The project has also expanded to a wider geographic and chronological framework to decode how Chinese civilization emerged and how its diverse elements formed a unity. Excavation of the Liangzhu site, which is over 5,000 years old and is one of the major sites covered in the origin-tracing project, has yielded an inner city covering 3 million square meters and an outer city of 6.3 million sq m, making it the world's largest capital at the time. It also had a giant water control system, which contributed to the formation of a rice-based agricultural society. By calculating the earthwork volume, archaeologists found that building the entire ancient city, the water control system and Mojiaoshan â a 10-meter-tall man-made terrace in the center of the city â required 10,000 people working daily for seven-and-a-half years. The discoveries show that Liangzhu had a kingship able to organize people for large-scale public construction, and its social differentiation, emergence of the city concept and existence of a kingship prove that it became a civilized society, said Wang Wei, a veteran archaeologist at the Chinese Academy of Social Sciences. Significant topic Wang said that tracing the origins of a civilization is a significant topic in the research of human history. Over the years, the Chinese project has provided China's answer to how to define civilizations. In 2022, Xi commended the efforts and stressed that the project has made creative contributions to the research on tracing the origins of the world's civilizations. Wang said: "International academia has proposed three indispensable elements for a civilized society based on features of Mesopotamian and Egyptian civilizations: written characters, metallurgy and the city concept. But we can find that some of the three elements were absent in many ancient civilizations. For example, the Mayan civilization had no metallurgy, while the Incan civilization didn't have written characters." Western scholars believe that Chinese civilization began with the Yinxu Ruins in Anyang, Henan province, a capital of the late Shang Dynasty (c.16th century-11th century BC), based on the discovery of inscribed oracle bones from that time. However, Chinese archaeologists don't agree. With continued archaeological research, international academia now believes that places around the world can propose criteria for civilization based on their own ancient social development. China's archaeological studies have shaped the nation's criteria in defining a civilization: the development of productivity, an increase in population, the appearance of cities, social differentiation and the emergence of kingship and state. "These criteria are suitable for identifying other civilizations as well," said Wang. "Civilizations have in common the appearance of kingship and state. They are only different in the ways of imposing kingship and the forms of state." In China, kingship and state "were shown by exquisite jade and bronze ritual artifacts, grand palaces and magnificent mausoleums imitating aboveground palaces", he added. "In Mesopotamia and ancient Egypt, they were demonstrated through superb stone temples, pyramids and large-scale tombs." Multidisciplinary subject President Xi said in 2020 that archaeologists should work closely with researchers from other fields to make an interpretive analysis of material remains. Zhang Chi, a professor of archaeology at Peking University, said that since material remains are often the research focus of archaeological studies, these should not only be observed with the eyes, but also studied using scientific and technological tools. Therefore, from the perspective of research methods, archaeology is by nature a multidisciplinary subject, Zhang added.
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 â˘(-9.8m/s2) â˘d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) â˘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.
Animal Rights and Diet Success Criteria I can explain key terms which describe the type of diets people have I can explain the advantages and disadvantages of different types of diet Animal Rights and Diet Match up the terms with the meaning Term Meaning Omnivore - eats fish but no other type of meat Vegetarian - eats most types of meat and vegetables Pescetarian - doesnât eat any products that come from animals Vegan - doesnât eat meat but will eat dairy products like milk Place the different diets on a spectrum All meat No animal products at all Vegetarian Vegan Omnivore Pescetarian Omnivore Omnivore Most people in the UK are omnivores Match the countries with the amount of meat eaten per person per year Country Meat per person per year India 9.9 kg USA 4.4 kg Bangladesh 120 kg UK 111.5kg Nepal 84.2 kg Australia 4 kg Numeracy How much meat is consumed in the UK per year? (Amount of meat eaten X the UK population) 2. How much meat is consumed in Bangladesh per year? (Amount of meat eaten X the Bangladesh population) Country Meat per person per year USA 120 kg Australia 111.5kg UK 84.2 kg Nepal 9.9 kg India 4.4 kg Bangladesh 4 kg UK â 64 million Bangladesh â 165 million http://www.telegraph.co.uk/travel/maps-and-graphics/world-according-to-meat-consumption/ 7 Why do people eat meat? Discuss Tradition (their family has always done it) Culture (celebrations) Taste Convenience Nutrients such as B12, protein and iron Consumption of meat is rising across developing countries because higher incomes generally mean more meat eating. Pescetarian "Yeah, I'm a vegetarian." "But that looks like fish you're eating." "Oh yeah, I eat fish.â An estimated 5% - 6% of people in the UK are pescetarians. How many people is this? Approx. 3.6 million Calculation â 66,000,000 /100 x 5.5 = 3,630,000 9 Which group is cuter? Animals Fish 10 People often donât feel as much love for fish as they do for fluffy, cute mammals. The may think fish donât feel pain. They may be fussy. They think fish isnât meat. Not farmed as much as mammals; can be wild. To get nutrients they wouldnât get from just vegetables and grains. (Omega 3 is in plants but in higher concentrations in oily fish) Why are people pescetarians? https://www.vegsoc.org/sslpage.aspx?pid=753 http://articles.mercola.com/omega-3.aspx Fish â In a perfect world, fish can provide you all the omega-3s you need. Unfortunately, the vast majority of the fish supply is now heavily tainted with industrial toxins and pollutants, such as heavy metals which include mercury, lead, arsenic, and cadmium, PCBs, and radioactive poisons. These toxins make eating fish no longer recommended. 11 Vegetarianism Vegetarians will not eat any meat or product that comes from the slaughter of animals e.g. gelatine. About 3% of the UK population are vegetarian. How many people is this? 1.9 million 12 Why are people vegetarian? They donât like the idea that animals are killed so they can eat Health reasons Donât like meat Brought up vegetarian Environmental reasons Religious reasons (e.g. some Buddhist, Hindus) Watch the following clip twice. The second time, write down the fact which surprises you the most. https://www.youtube.com/watch?v=VW6wfpHFdaI The World Health Organization has classified processed meats â including ham, salami, sausages and hot dogs â as a Group 1 carcinogen (same as smoking/alcohol) which means that there is strong evidence that processed meats cause cancer. Red meat, such as beef, lamb and pork has been classified as a 'probable' cause of cancer. 13 Veganism Not just a diet Around 1% of the population of UK are vegans. A vegan is described by the Vegan Society as âa philosophy and way of living which seeks to excludeâas far as is possible and practicableâall forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of humans, animals and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animalsâ Why are people vegan? Why are people vegan? James Aspey: https://www.youtube.com/watch?v=a22XxXP3nU8 Warning: some of the content in this video clip may upset some viewers from 7:14 â 8:11 https://www.youtube.com/watch?v=BtqXeym7H8A Why are people vegan? âDonât want bad karmaâ Feel healthier Reduce chances of diseases. Example heart disease. Donât want to exploit animals Believe in animal rights Sustainability Environment Create a Table of Pros & Cons of Veganism Pros â Cons - Create a Table of Pros & Cons of Veganism Pros Cons No animals have died for you to eat Some people think it is healthier Help the environment Fewer antibiotics/chemicals that are given to some animals Makes you feel good No vitamin B12 so have to supplement Harder to find food at shops or restaurants May be harder to get enough iron May be more expensive to get substitute meats Judged by family and friends Could put farmers out of business Group Work Source 1 Summarise it in your jotter Explain what the source is/what it says What does it suggest? What is your opinion? Feedback to rest of class https://www.youtube.com/watch?v=SYyjel5VuHg Farmerâs Poem