A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ________ m.

Solution

Physics sir · 4 steps

Restitution scales the speed, and height goes as speed squared, so the height scales by e².

1. Speed before impact. Falling from rest through h = 20 m, the ball hits the floor with u = √2gh.
2. Speed after impact. The floor does not move, so restitution gives the rebound speed directly: v = e u. The ball leaves the floor with half the speed it arrived with.
3. Rebound height. It rises until that speed is used up, so h' = v²/2g = (e² u²)/2g. Since u² = 2gh, the 2g cancels.

   h' = e² h = (0.5)² × 20 = 0.25 × 20 = 5 m

4. So. The ball rebounds to a height of 5 m.

The common slip: 10. Multiplying the height by e instead of e² gives 10. Restitution scales speed, and height depends on speed squared.

The idea to keep. For a ball bouncing off a fixed floor, each bounce multiplies the speed by e and the height by e². You do not need g at all.

Answer from the NTA final answer key. Solution by PrepWiser.