A 1kg ball moving at $17m{s}^{-1}$ collides head on with a 2kg ball moving in the opposite direction at $22m/s.$ The velocity of each ball after the impact, if the coefficient of restitution is $2/3,$ is

$1\times 17-2\times 22=1\times v_1+2v_2$ ……..(1)

$\frac{1}{2}{m}_1\left(v_1^2-u_1^2\right)=\frac{1}{2}{m}_2\left(v_1^2-u_1^2\right)$

$v_2-v_1=26$ $-0.3-v_1=26$

$v_2-v_1=\frac{2}{3}\left(39\right)=26$                         $v_1=-26.03$

(1) $\Rightarrow v_1+2v_2=27$                             $v_1=-26.3$

$\frac{-v_1-v_2=26}{3v_2=-1}$

$v_2=\frac{-1}{3}=-0.3m/s$