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Projectile MotionHow does the velocity of a projectile determine its shape?When you watch a football game, you notice that when the punter kicks the football, it always travels the same shaped path, or trajectory. Projectile motion describes the trajectory of the football. The trajectory of the football can be described by both its horizontal (x) and vertical (y) locations over time.Why?For a football that is kicked, it moves both horizontally and vertically. Given below is a model of a football from an opening kickoff. Model 1: Location of a Football Over Time3057525212725361950312610558388253059430492442516973551266825168783039433502590802181225278130What is the football’s horizontal location at 1.0 seconds?What is the football’s horizontal location at 1.5 seconds?How far did the football travel horizontally from t = 1.0 sec to t = 1.5 sec? How far did the football travel horizontally from t = 2.0 sec to t = 2.5 sec? -38100151765Is the football’s horizontal velocity constant, or is it accelerating? Calculate the horizontally velocity of the football from t = 0 sec to t = 3.0 sec. Show all calculations below.What is the football’s vertical location at 0 seconds?What is the football’s vertical location at 0.5 seconds?How far did the football travel vertically from t = 0 sec to t = 0.5 sec? How far did the football travel vertically from t = 0.5 sec to t = 1.0 sec? 19050-91440Is the football’s vertical velocity constant or is it accelerating in the vertical direction? At what time does the football reach its maximum height?What is the vertical velocity of the football at its maximum height? Consider this your final vertical velocity.171450160020Determine the initial vertical velocity of the football at t = 0 sec using equations from linear motion.As a team, use your answer from question #13 to choose an equation to solve for the initial vertical velocity of the football. Write your equation below.Have the technician calculate vertical velocity at t = 0 sec using equations from linear motion. Show all of your calculations below. Determine the acceleration of the football from t = 0 seconds to t = 1.5 seconds using equations from linear motion.As a team, use your answer from questions #13 and question #14 to choose an equation to solve for the acceleration of the football. Write your equation below.Have the technician calculate the vertical acceleration of the football using equations from linear motion, and show the steps to the calculation below. 19050-3810What do you notice about the vertical acceleration of the football? What do you call this number?Extension QuestionsFor the example of the football, it was assumed that there was no air resistance. Air resistance is a force that counteracts the motion of an object moving through the air. In a real situation, air resistance would be present in the football’s motion. As a team, discuss what would change about the football’s trajectory if air resistance was taken into account.23812523495Learning ObjectivesAfter completing the activity, the students should be able to:Content:Apply information learned from linear motion to projectile motion.Determine that a projectile moves at a constant horizontal velocity.Determine that a projectile accelerates at 9.81 m/s2 in the vertical direction.ProcessWork as a team to process information from a diagram.Use data from a model to solve for velocity and acceleration of a projectile.PrerequisitesStudents will have previously learned about linear motion including velocity and acceleration. Previous knowledge would have been gained through a previous POGIL as well as laboratory exercises and class discussions.Assessment QuestionsWhat is the vertical acceleration of a projectile? (a)9.81 m/s2; downward9.81 m/s2; left9.81 m/s2; right9.81 m/s2; upwardIn which direction does the velocity remain constant? (horizontal)During a baseball game, a ball is hit to a maximum height of 25 meters. If it takes the ball 3 seconds to reach its maximum height, what is the initial vertical velocity of the baseball? (23.05 m/s)Teacher TipsThe teacher should stress that the horizontal and vertical directions are independent of one another. To get the overall velocity, the horizontal and vertical components of the velocity can be added together using the Pythagorean Theorem. Use students’ prior knowledge of adding displacements to help them find the resultant velocity.Target AudienceThis activity is designed to be used in a first year honors physics class. Further lessons will be given in the form of laboratory exercises which will allow students to apply the information gained from this activity. ................
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