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.
Initial momentum of the system = 0
Final momentum of the system = 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 / M
= 0.020 × 80 / (100 × 1000)
= 0.016 m/s