Two spheres A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along X-axis. After collision, B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction 

Initial momentum, ${\mathrm{p}}_{\mathrm{i}}={\mathrm{m}}_2\mathrm{v}\hat{\mathrm{i}} + {\mathrm{m}}_1\times 0$

Final momentum, ${\mathrm{p}}_{\mathrm{f}}={\mathrm{m}}_2(\mathrm{v}/2)\hat{\mathrm{j}} + {\mathrm{m}}_1\times {\mathrm{v}}_1$

From law of conservation of momentum,

                             ${\mathrm{p}}_{\mathrm{i}}={\mathrm{p}}_{\mathrm{f}}$

                     ${\mathrm{m}}_2\mathrm{v}\hat{\mathrm{i}}={\mathrm{m}}_2\frac{\mathrm{v}}{2}\hat{\mathrm{j}}+{\mathrm{m}}_1\times {\mathrm{v}}_1$

                          ${\mathrm{v}}_1=\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\mathrm{v}\hat{\mathrm{i}}-\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\frac{\mathrm{v}}{2}\hat{\mathrm{j}}$

From this equation, we can find, $\mathrm{tan\theta }=\frac{1}{2}$

$\Rightarrow$                      $\mathrm{\theta } = {\tan }^{-1}\left(\frac{1}{2}\right)$ to the X-axis.