A football player of mass 129 kg is running at a speed of 7.7 m/s when he catche

Question

A football player of mass 129 kg is running at a speed of 7.7 m/s when he catches a ball thrown by the quarterback. The mass of the ball is 0.41 kg it has a speed of 22.0 m/s just before the player caught it. Assuming that the football player catches the ball with his feet off the ground and both the player and ball are moving horizontally, calculate the final velocity of the ball and player. Calculate the loss of kinetic energy in this case. Instead, the ball was intercepted by the safety of the same mass but running in the opposite direction at the same speed of 7.7 m/s. What is the final speed in this situation? What is the loss in kinetic energy for the second case? (Might the loss of kinetic energy be related to how much it hurts to catch the pass?)

Explanation / Answer

using conservation of momentum

part a )

m1v1 + m2v2 = (m1 + m2) vf

vf = 129 * 7.7 + 22 * 0.41 / ( 129 + 0.41 )

vf = 7.745 m/s

part b )

lost in kE = 1/2 * (m1 + m2 ) vf^2 - (1/2 m1v1^2 + 1/2 m2 v2^2 )

= -42.09 J

part c )

if they are in oppoite direction

vf = 129 * 7.7 - 0.41 * 22 / 129.41

vf = 7.61 m/s

part d )

change in kinetic energy

= 1/2(m1+m2)vf^2 - 1/2 m1v1^2 + 1/2m2v2^2

= -176.22 J

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