A 1kg ball moving at 12 ms−1 collides head on with a 2kg 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

m_{1} = 1 kg, u_{1} = 12 m/s

$m_{2} = 2 kg, u_{2} = - 24 m/s$

$e = \frac{2}{3}$

$v_{1} = \frac{(m_{1} - {em}_{2}) u_{1}}{m_{1} + m_{2}} + \frac{(m_{1}) (1 + e) (u_{2})}{m_{1} + m_{2}}$

$= \frac{(1 - \frac{4}{3}) 12}{3} + \frac{1 (1 + \frac{2}{3}) (- 24)}{3}$

$= \frac{\frac{- 1}{3} \times 12}{3} + \frac{2 \times \frac{5}{3} \times - 24}{3}$

$= \frac{- 4}{3} + \frac{- 80}{3}$

$= \frac{- 84}{3}$

$v_{1} = - 28 m/s$

$v_{2} = \frac{m_{1} (1 + e) u_{1}}{m_{1} + m_{2}} + \frac{(m_{2} - {em}_{1}) u_{2}}{m_{1} + m_{2}}$

$= \frac{1 (1 + \frac{2}{3}) 12}{3} + \frac{(2 - \frac{2}{3})}{3} - 24$

$= 1 \times \frac{5}{3} \times 12 \times \frac{1}{3} + \frac{4}{3} \times - 24 \times \frac{1}{3}$

$= \frac{20}{3} + (\frac{- 32}{3})$

$v_{2} = \frac{- 12}{3} = - 4 m/s$

A 1kg ball moving at $12 {ms}^{- 1}$ collides head on with a 2kg 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