A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s^–1, what is the recoil speed of the gun?

Mass of the shell, m = 0.020 kg
Muzzle speed of the shell, v = 80 m/s
Recoil speed of the gun = V

Both the gun and the shell are at rest initially.
Initial momentum of the system = 0
Final momentum of the system = mv – MV

Here, the negative sign appears because the directions of the shell and the gun are opposite to each other.
Now, as per the law of conservation of momentum. we have
Final momentum = Initial momentum 
 
          mv – MV = 0 
∴                   V = mv / M 

                       = 0.020 × 80 / (100 × 1000)
                       = 0.016 m/s