Question

Calculate the recoil velocity of a 5 kg rifle that fires a 24 g bullet that travel 1.5 m in 0.0023 s

Answer 1

The mass of rifle is M = 5kg . It fires the bullet of mass m =24 g = 0.024 kg

It travels a distance, d = 1.5 m and the time taken is t = 0.0023 s

The speed of the bullet will be

$\begin{gathered} v=\frac{d}{t} \\ =\frac{1.5}{0.0023} \\ =652.17\text{ m/s} \end{gathered}$

Let the recoil velocity be V. The initial velocity will be zero as rifle and bullet are at rest.

According to the conservation of momentum

$\begin{gathered} \text{Initial momentum = final momentum} \\ (M+m)\times0=MV-mv\text{ } \end{gathered}$

Here, rifle and bullet travel in opposite directions.

Substituting the values, the recoil velocity will be

$\begin{gathered} V=\frac{mv}{M} \\ =\frac{0.024\times652.17}{5} \\ =3.13\text{ m/s} \end{gathered}$