a gun of mass 1000 kg fires a shell of mass 2 kg with a velocity of 200 m/s. calculate the velocity of recoil of the gun.
Mass of gun is, mg = 1000 kg
Mass of shell, ms = 2 kg
Velocity of the shell, vs = 200 m/s
Recoil velocity of the gun is say v
Now, momentum of the system before firing = 0 [since all were at rest]
Momentum of the system after firing = (2)(200) + (1000)(V) = 400 + 1000V
By law of conservation of momentum,
400 + 1000V = 0
=> V = -0.4 m/s
[the negative sign indicates that velocity of gun is opposite to the velocity of the shell]