A ball is dropped from a height h on a floor. The coefficient of restitution for the collision between the ball and the floor is e . The total distance covered by the ball before it comes to the rest.

Step-by-step solution

Height achieved in n t h collision is given by h n = e 2 n h Distance covered in first collision = h , Distance covered in 2 nd collision = 2 e 2 h , and so on. Total distance covered by the ball before it comes to rest: s = h + 2 e 2 h + 2 e 4 h + . . . . . . ⇒ s = h 1 + 2 e 2 + 2 e 4 + 2 e 6 + . . . . . . from the sum of infinite geometric progression: ⇒ s = h 1 + 2 e 2 1 - e 2 ⇒ s = h 1 + e 2 1 - e 2