A bullet of mass $50 g$ going at a speed of $200\mathrm{ }\mathrm{m}{\mathrm{s}}^{-1}$ strikes a wood block of mass 950 gm and gets embedded in it. The velocity of the block after the impact is

The two diagrams show the situation before and after a collision between two spheres $\mathrm{A}$ and $\mathrm{B}$ of equal radii moving along the same straight line on a smooth horizontal surface. The coefficient of restitution $e$ is

A particle strikes a horizontal frictionless floor with a speed $u$ at an angle $\mathrm{\theta }$ with the vertical, and rebounds with a speed $v$at an angle $\varphi$ with vertical. The coefficient of restitution between the particle and floor is $e$. The angle $\varphi$ is equal to