Mass of the gun, M=100 kg
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.
The initial momentum of the system m=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.
According to the law of conservation of momentum:
Final momentum = Initial momentum
mv−MV=0
V=mv/M
V=0.02×80100=0.016 m/s