Question

A standard rifle has a mass of 2.69 kilograms. If it were used to fire an "elephant gun" round of mass 69.4 grams at +650 meters per second, what would be the recoil velocity of the rifle? Include units in your answer. More information.

Answer 1

Initially, the system is at rest therefore, the initial momentum of the system is zero.

The final momentum of the system can be expressed as,

`p_f=m_1v_1+m_2v_2`

According to conservation of momentum,

`p_i=p_f`

Plug in the known expressions,

`\begin{gathered} 0=m_1v_1+m_2v_2 \\ m_1v_1=-m_2v_2 \\ v_1=-(m_2)/(m_1)v_2 \end{gathered}`

Substitute the known values,

`\begin{gathered} v_1=-\frac{(69.4\text{ g)(}\frac{1\text{ kg}}{1000\text{ g}})}{(2.6\text{9 kg)}}(650\text{ m/s)} \\ =-16.8\text{ m/s} \end{gathered}`

Thus, the recoil velocity of gun is -16.8 m/s where negative sign indicates that the motion of rifle is in the opposite direction of the bullet.