A particle at rest is constrained to move on a smooth horizontal surface. Another identical particle hits the stationary particle with a velocity v at an angle $\mathrm{\theta }={60}^{\circ }$ with horizontal. If the particles move together, the velocity of the combination just after the impact is equal to

The impact takes place along the line joining them. Since the particle at rest is constrained to move on the horizontal surface, we cannot conserve the momentum along the line joining them. Since no net force is acting on the system of particles parallel to the surface, conservation of linear momentum along that direction yields

$\mathrm{mvcos}\mathrm{\theta }=(\mathrm{m}+\mathrm{m}){\mathrm{v}}^{\mathrm{\prime }}\Rightarrow {\mathrm{v}}^{\mathrm{\prime }}=\frac{\mathrm{v}}{2}\cos {60}^{\circ }=\frac{\mathrm{v}}{4}$