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Velocity of COM

A 1kg ball ...

Question

A $1$ kg ball moving at $12 m s^{- 1}$ collides head on with a $2$ kg ball moving in the opposite direction at $24 m / s$ . The velocity of each ball after the impact, if the coefficient of restitution is $2 / 3$ , is?

- 28 m / s; - 4 m / s

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- 20 m / s; - 4 m / s

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20 m / s; 24 m / s

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28 m / s, - 4 m / s

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Solution

The correct option is A $- 28 m / s; - 4 m / s$
Given : Coefficient of restitution $e = \frac{2}{3}$
Velocity of mass $1 k g$ after the collision is given by
$V_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$
Or $V_{1} = \frac{(1 - \frac{2}{3} \times 2) \times 12 + (1 + \frac{2}{3}) \times 2 \times (- 24)}{1 + 2} = - 28 m / s$
Velocity of mass $2 k g$ after the collision is given by
$V_{2} = \frac{(m_{-} e m_{1}) u_{2} + (1 + e) m_{1} u_{1}}{m_{1} + m_{2}}$
Or $V_{2} = \frac{(2 - \frac{2}{3} \times 1) \times (- 24) + (1 + \frac{2}{3}) \times 1 \times (12)}{1 + 2} = - 4 m / s$

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A 1kg ball moving at 12ms−1 collides head on with a 2kg ball moving in the opposite direction at 24m/s. The velocity of each ball after the impact, if the coefficient of restitution is 2/3, is?

A $1$ kg ball moving at $12 m s^{- 1}$ collides head on with a $2$ kg ball moving in the opposite direction at $24 m / s$ . The velocity of each ball after the impact, if the coefficient of restitution is $2 / 3$ , is?