Question

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 $m\,s^{-1}$, 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.
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
$\therefore V$ = $\frac{mv}{M}$

= $\frac{0.020\times 80}{100\times 1000}$

= 0.016 m/s