Aball is dropped from rest onto a fixed horizontal surface and rebounds to a height which is 64% of its original height. (a) what is the coefficient of restitution? (b) with what vertical velocity must the ball strike the surface to rebound to a height of 25 ft?

(a) The coefficient of restitution is 0.8.

(b) The ball must strike the surface with a 50.14 ft/s vertical velocity, approximately.

Explanation:

The ratio between the final and the initial height is given by

Before the impact, we have

Analogously after the impact

From the previous, the restitution coefficient can be calculated from the ratio between the ball's velocity, after and before the impact, i.e.

If the ball is meant to rebound to a 25 ft height, we plug in this value in one of the previous equations as follows

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