First slide

Types of collision

Question

A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is

Moderate

A

$20 {ms}^{- 1}$
B

$15 {ms}^{- 1}$
C

$10 {ms}^{- 1}$
D

$5 {ms}^{- 1}$

Solution

Let ball is projected vertically downward with velocity v from height h
Total energy at point A = $\frac{1}{2} {mv}^{2} + mgh$
During collision loss of energy is 50% and the ball rises up to same height. It means it possess only potential energy at same level.
$\begin{array}{l} 50 % (\frac{1}{2} {mv}^{2} + mgh) = mgh \\ \frac{1}{2} (\frac{1}{2} {mv}^{2} + mgh) = mgh \end{array}$
$v = \sqrt{2 gh} = \sqrt{2 \times 10 \times 20}$
v = 20 m/s

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