A shell of mass 0.020 kg is fired by a gun of mass 100 kg.

Question.
A shell of mass $0.020 \mathrm{~kg}$ is fired by a gun of mass $100 \mathrm{~kg}$. If the muzzle speed of the shell is $80 \mathrm{~m} \mathrm{~s}^{-1}$, what is the recoil speed of the gun?

solution:

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 – 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

$\therefore V=\frac{m v}{M}$

$=\frac{0.020 \times 80}{100 \times 1000}=0.016 \mathrm{~m} / \mathrm{s}$