A football player throws a 420 g football at 40 degree to the horizontal. Being

Question

A football player throws a 420 g football at 40 degree to the horizontal. Being in a good physical condition, he is able to develop 200 W of power for the 0.6 seconds that it takes him to throw the ball. The ball is caught at exactly the same height above the ground as it was thrown Full points will be awarded for the correct answer to the following questions: How far does the ball travel in the horizontal direction? ___ If the full credit cannot be awarded, then partial credit will be awarded for the correct answers to the following questions: i) What is the initial kinetic energy of the football? ___ ii) How much work did the player applied to the football? ___ iii) What is the kinetic energy of the football immediately after the player threw it? ___ iv) What is the speed of the ball (immediately after it has separated from the athlete's hand)? ___ v) What is the vertical component of the ball's velocity?___ vi) What is the value of vertical acceleration of the ball? ___ vii) How long will it take for the ball to get to the maximum height? ___ viii) How long will it take for the ball to get up to the maximum and then fall back to the initial height? ___ ix) What is the horizontal component of the ball's velocity? ___ x) How far will the ball travel in the horizontal direction within the time found in viii)? ___

Explanation / Answer

power = 200 w

time t - 0.6 s

work done = 200*0.6 = 120 J

KE of the ball immediately aftr throw K = 120 J

speed of the ball v = sqrt(2 K/m) = sqrt(2*120/0.42) = 23.9 m/s

vertical comp of the vel. vy = 23.9Sin(40) = 15.36 m/s

vertical acceleration = -g = -9.8m/s2

when reached maximum height vel v=0

0 = 15.36 -9.8t ; t = 1.57 s , to reach max. height

time to reach the same height back = 2*1.57 = 3.14 s

horizontal comp. of vel. = 23.9Cos(40) = 18.31 m/s

horizontal distance traveled in the time = 18.31*3.14 = 57.49 m

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