A small smooth disc of mass m and radius r moving with an initial...

The larger disc will move along line of impact

As $e = 0$, so velocity of larger disc

$v^{′} = \dfrac{\text{mv cos} \theta}{\text{m} + 2 \text{m}} = \dfrac{\text{v cos} \theta}{3}$

Velocity of larger disc

= v^{'}\text\cos\theta\overset{^}{i} - v^{'}\text\sin\theta\overset{^}{j}

= \dfrac{v}{3}\cos^{2}\theta\overset{^}{i} - \dfrac{v}{3}\text\sin\theta\text\cos\theta\overset{^}{j}

( from the figure we can calculate $cos\theta = \dfrac{2\sqrt{2}}{3}$, $sin\theta = \dfrac{1}{3}$ )

= \dfrac{8}{27}\text{v}\overset{^}{i} - \dfrac{2\sqrt{2}}{27}\text{v}\overset{^}{j}