A ball is bouncing down a set of stairs. The coefficient of restitution is e. The height of each step is d and the ball bounces one step at each bounce. After each bounce the ball rebounds to a height h above the next lower step. Neglect width of each step in comparison to h and assume the impacts to be effectively head on. Which of the following relative is correct ?

Options

A. `(h)/(d) = 1 - e^(2)`
B. `(h)/(d) = 1 - e`
C. `(h)/(d) = (1)/(1 - e^(2))`
D. `(h)/(d) = (1)/(1 - e)`

Answer

C

Explanation

`sqrt(2g (h - d)) = esqrt(2gh) rArr (h)/(d) = (1)/(1 - e^(2))`