Ball Dropped and Rebounding with Energy Loss – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Collision

Ball Dropped and Rebounding with Energy Loss

A ball is thrown vertically downwards from a height of $20\text{ m}$ with an initial velocity $u_0$. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $u_0$ is: (Take $g = 10\text{ ms}^{-2}$)

(2015 Re)

$10\text{ m/s}$
$14\text{ m/s}$
$20\text{ m/s}$
$28\text{ m/s}$

Solution:

The velocity just before impact is $v^2 = u_0^2 + 2gh$. Since it loses $50\%$ energy and reaches the same height $h$, the post-collision kinetic energy satisfies $mgh = \frac{1}{2}(\frac{1}{2}mv^2)$, leading to $v^2 = 4gh$. Solving gives $u_0 = \sqrt{2gh} = 20\text{ m/s}$.

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