${\mathrm{V}}_{{\mathrm{y}}_1}={\mathrm{V}}_{{\mathrm{y}}_2}$

⇒ 10 sin 60° = u sin 30°

$\Rightarrow \mathrm{u}=10\sqrt{3}\mathrm{m}/\mathrm{s}$

motion in x and y direction of centre of mass is not affected by collision.

${\mathrm{u}}_{\mathrm{cy}}=\frac{{\mathrm{mu}}_{1\mathrm{y}}+{\mathrm{mu}}_{2\mathrm{y}}}{2\mathrm{m}}=\frac{10\sin {60}^{\circ }+10\sqrt{3}\sin {30}^{\circ }}{2}=5\sqrt{3}\mathrm{m}/\mathrm{s}$

time of flight of CM = 2 × $\frac{5\sqrt{3}}{10}=\sqrt{3}\text{ sec. }$

S_cx = u_cx × t

${\mathrm{u}}_{\mathrm{cx}}=\frac{{\mathrm{mu}}_{1\mathrm{x}}+\mathrm{mu}}{2\mathrm{m}}=\frac{10\cos {60}^{\circ }-10\sqrt{3}\cos {30}^{\circ }}{2}=-5\mathrm{m}/\mathrm{s}$

${\mathrm{S}}_{\mathrm{cx}}=-5\mathrm{m}\sqrt{3}$

Initial position of COM is midway

Final position =  $5\sqrt{3}-5\sqrt{3}=0$