The initial velocity of both the gun and the shell system is zero

The initial momentum of the system = 0

Given,

Mass of the gun, M = 100 kg

Mass of the shell, m =0.02 kg

Final speed of the muzzle of the shell, v = 80 m/s

We suppose the recoil speed of the gun to be V.

The final momentum of the system = mv – MV

The negative sign is because the direction of motion of gun and shell is opposition to each other.

According to the law of conservation of linear momentum:

Total initial momentum = Total final momentum

Therefore,

0 = mv – MV

⇒

⇒ = 0.016 m/s

The recoil speed of the gun is 0.016 m/s