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 seed of gun is `v`. Taking gun`+`bullet as the system. Net external force on the system in horizontal directioin zero.
initial the system was rest. Therfore, applying the principle of conservation of inear momentum in horizontal direction, we get
`Mv-m(v_(r)cos60^(@)-v)+0`
`:. v=(mV_(r)cos60^(@))/(M+m)`
or `v=(mV_(r))/(2(M+m))`