A certain ball has the property that each time it falls from a height onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters.
(a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels. (Use the fact that the ball falls ½ gt2 meters in t seconds)
(b) Calculate the total time that the ball travels.
(c) Suppose that each time the ball strikes the surface with velocity it rebounds with velocity – kv, where 0 < k < 1. How long will it take for the ball to come to rest?