Problem 74E

74. A certain ball has the property that each time it falls from a height $h$ onto a hard, level surface, it rebounds to a height $r h$, 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.

(b) Calculate the total time that the ball travels. (Use the fact that the ball falls $\frac{1}{2} g t^{2}$ meters in $t$ seconds.)

(c) Suppose that each time the ball strikes the surface with velocity $v$ it rebounds with velocity $-k v$, where $0<k<1$. How long will it take for the ball to come to rest?

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