Question

A ball moving at a velocity v = 10 m/s hits the foot of a football player. 

Determine the velocity u with which the foot should move for the ball impinging on it to come to a halt, assuming that the mass of the ball is much smaller than the mass of the foot and that the impact is perfectly elastic.

Answer 1

If the foot of the football player moves at a velocity u at the moment of kick, the velocity of the ball is v + u (the axis of motion is directed along the motion of the ball) in the reference frame fixed to the foot of the player. After the perfectly elastic impact, the velocity of the ball in the

same reference frame will be - (v + u), and its velocity relative to the ground will be - (v + u) - u. If the ball comes to a halt after the impact, v + 2u = 0, where u = -v/2 = -5 m/s. The minus sign indicates that the foot of the sportsman must move in the same direction as that of the ball before the impact.