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 relation is correct ?

Options

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

Answer

A

Explanation

The ball falls a distance h from its highest (rest) position and rebounds a distance (h - d).
Thus the coefficient of restitution `e=sqrt((h-d)/(h))`
`e^(2)=(h-d)/(h)orh=(d)/(1-e^(2))`