A body is dropped from a height h on an inelastic floor. If the coefficient of restitution is e, then find the height of the body after nth collision.

Let v₀ and v₁ be the velocities of body just before and after collision when it hits first time.
By definition, coefficient of restitution is given by
                     
                                      ...(1) 
The velocity of rebound after first collision is v₁, therefore second time it will hit the ground with velocity v_1. 
Let after collision it rebound with velocity v₂. 
i.e.,                     
                              ...(2) 
Similarly, the velocity of body after third fourth.....nth collision is, 
 , , ....         ...(3) 
As the body falls from height h, therefore it will hit first time with velocity v₀ given by 
                                          ...(4) 
After nth collision, it rebounds with velocity v_n and let it attain the height h₀.
Thus, 
                                         ...(5) 
Now from (3), 
                                           ...(6) 
From (4) and (5), 
                                          ...(7) 
∴                 , is the height of the body after the n^th collision.