Question

A shell of mass $0.020kg$ is fired by a gun of mass $100kg$. If the muzzle speed of the shell is $80m/s$, what is the recoil speed of the gun?

Answer 1

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

$mv-MV=0$

$V=mv/M$

$V=0.02\times \frac{80}{100}=0.016m/s$