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

Given,

Coefficient of restitution $e=\frac{2}{3}$

Following the collision, the velocity of a mass of 1 kg is given by

${\mathrm{v}}_1=\frac{({\mathrm{m}}_1-{\mathrm{em}}_2){\mathrm{u}}_1+(1+\mathrm{e}){\mathrm{m}}_2{\mathrm{u}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

${\mathrm{v}}_1=\frac{\left(1-{\displaystyle \frac{2}{3}}\times 2\right)\times \left(12\right)+\left(1+{\displaystyle \frac{2}{3}}\right)\times 1\times -24}{1+2}=-28\mathrm{m}/\mathrm{s}$

Following the collision, the velocity of a mass of 2kg is given by

${\mathrm{v}}_2=\frac{({\mathrm{m}}_2-{\mathrm{em}}_1){\mathrm{u}}_2+(1+\mathrm{e}){\mathrm{m}}_1{\mathrm{u}}_1}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

${\mathrm{v}}_2=\frac{\left(2-{\displaystyle \frac{2}{3}}\times 1\right)\times (-24)+\left(1+{\displaystyle \frac{2}{3}}\right)\times 2\times \left(12\right)}{1+2}=-4\mathrm{m}/\mathrm{s}$

Hence the correct answer is -28m/s, -4m/s.