A ball is bouncing down a flight of stairs. The coefficient of restitution is e. The height of each step is d and the ball descends one step each bounce. After each bounce it rebounds to a height h above the next lower step. The height is larger enough compared with the width of step so that the impacts are effectively head-on. Find the relationship between h and d.

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))`