find out the recoil-velocity of the gunas shell

Question

Find out the recoil-velocity of the gun:

As shell of mass 200 gm is fired at a velocity of 50 metres/second by a gun of mass 20 kg. Find out the recoil-velocity of the gun.

Solution

Since initially shell and gun both are at rest

m_g V_{g (2)}  + m_s V_{s (1)}  = 0

∴ V_{g (2)}  = recoil of gun = - (m_s V_{s (2)}  )/m_g

= (0.2 × 50 )/20

 = - 0.5 m / sec.

Negative sign defined that the gun moves in a direction opposite to that of the shell since reaction on the gun is along opposite direction to the motion of shell.