A small smooth disc of mass m and radius r moving with an initial velocity v along the positive x -axis…

The larger disc will move along line of impact

As  $\mathrm{e}=0$, so velocity of larger disc

   ${\text{v}}^{\prime }=\frac{\text{mv cos }\theta }{\text{m}+2\text{m}}=\frac{\text{v cos }\theta }{3}$

Velocity of larger disc

        $={\text{v}}^{\text{'}}\text{cos }\mathrm{\theta }\hat{\mathrm{i}}-{\text{v}}^{\text{'}}\text{sin }\mathrm{\theta }\hat{\mathrm{j}}$

        $=\frac{\text{v}}{3}{\text{cos}}^2\mathrm{\theta } \hat{\mathrm{i}}-\frac{\text{v}}{3}\text{sin}\mathrm{\theta } \text{cos }\mathrm{\theta }\hat{\mathrm{j}}$ 

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

        $=\frac{8}{27}\text{v }\hat{\mathrm{i}}-\frac{2\sqrt{2}}{27}\text{v }\hat{\mathrm{j}}$