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JH

# 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 $rh,$ 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.(b) Calculate the total time that the ball travels. (Use the fact that the ball falls $\frac {1}{2} gt^2$ meters in $t$ seconds.)(c) Suppose that each time the ball strikes the surface with velocity $v$ it rebounds with velocity $-kv,$ where $0 < k < 1.$ How long will it take for the ball to come to rest?

## (A). $D=\frac{H(1+r)}{1-r}$(B). $\sqrt{\frac{2 \mathrm{H}}{\mathrm{g}}} \cdot \frac{1+\sqrt{\mathrm{r}}}{1-\sqrt{\mathrm{r}}}$(C). $\mathbf{T}=\frac{\mathbf{v}}{\mathbf{g}} \cdot \frac{1+\mathbf{k}}{1-\mathbf{k}}$

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Missouri State University

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