A gun (mass=M) fires a bullet (mass=m) with speed `v_r` relative to barrel of the gun which is inclined at an angle of `60^@` with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of gun.

Explanation

Let the recoil speed of gun is v. Taking gun + bullet as the system. Net external force on the

system in horizontal direction is zero. Initially the system was at rest. Therefore, applying the principle of conservation of linear momentum in horizontal direction, we get
`Mv-m(v_(r)cos60^(@)-v)=0`
`thereforev=(mv_(r)cos60^(@))/(M+m)`
or `v=(mv_(r))/(2(M+m))`