Question

A ball is dropped from a height h on a horizontal plane and the coefficient of restitution for the impact is e, the velocity with which the ball rebounds from the floor is

• A. eh
• B. egh
• C. $e\sqrt{gh}$
• D. $e\sqrt{2gh}$

Answer 1

Answer: (D)

$e\sqrt{2gh}$

Answer 2

Let u be the velocity with which the ball strikes the ground. Then, $u^{2} = 2gh$ ⇒ $u = \sqrt{2gh}$ .....(i)

Suppose the ball rebounds with velocity v, then $V = - e( - u - 0)$ ⇒ $v = ue$ ⇒ $v = e\sqrt{2gh}$, [from (i)].