First slide

Coefficient of restitution

Question

A ball moving with velocity $9 {ms}^{- 1}$ collides with another similar stationary ball. If after the collision, both the balls move in directions making an angle of 30° with the initial direction, then their speeds after collision will be

Moderate

A

$5.2 {ms}^{- 1}$
B

$0.52 {ms}^{- 1}$
C

$52 {ms}^{- 1}$
D

$26 {ms}^{- 1}$

Solution

The given condition as shown in the figure below.
After collision, ${mv}_{1} sinθ = {mv}_{2} sinθ \Rightarrow v_{1} = v_{2} = v$
$∴$ $2 mv \cos θ = m \times 9$
$\Rightarrow$ $2 v \cos 30 ° = 9$
$\Rightarrow$ $v= \frac{9}{\sqrt{3}} = 3 \sqrt{3} = 5.2 m s^{- 1}$

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