First slide

Coefficient of restitution

Question

A ball falling freely from a height of 4.9 m ,hits a horizontal surface. If e = 3/4, then the ball will hit the surface second time after

Moderate

A

1 s
B

1.5 s
C

2 s
D

3 s

Solution

Velocity on hitting the surface
$= \sqrt{2 gh} = \sqrt{2 \times 9.8 \times 4.9}$
$= 9.8 {ms}^{- 1}$
Velocity after first bounce, $v = \frac{3}{4} \times 9.8 {ms}^{- 1}$
Time taken from first bounce to the second bounce $= \frac{2 v}{g}$
$= 2 \times \frac{3}{4} \times 9.8 \times \frac{1}{9.8} = 1.5 s$

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