A ball is let fall from a height h₀ . It makes n collisions with the earth. After n collisions it rebounds with a velocity v_n and the ball rises to a height h_n , then coefficient of restitution is given by

Step-by-step solution

The velocity of ball after n th rebound will be v_n=e^n v₀ ( where v₀= 2 g h₀ ) Therefore, the height after n th rebound will be aligned h_n & = v_n^2 2 g = e^ 2 n v₀^2 2 g = e^ 2 n 2 g h₀ 2 g e^ 2 n & = h_n h₀ or e= [ h_n h₀ ]^ 1 / 2 n aligned