Question

A bullet is fired with a velocity \[v\] from a gun of mass \[M\] . What will be the recoil velocity of the gun if the mass of the bullet is \[m\] ?

Answer 1

Hint: Recoil is the phrase for a rifle kicking backwards. The rearward force implied by the gun as the bullet is discharged, in theory, is what conserves linear momentum. According to Newton's Third Law, when a force, known as the action force, is applied to an accelerating bullet, there will be an equal and opposite force, known as the reaction force, which causes the recoil.

Complete step by step answer:
A gun's recoil is an example of linear momentum conservation. When a bullet is fired, a gun always recoils to conserve linear momentum. The total momentum of the gun and the bullet before and after firing will be equal, according to the Law of Conservation of Momentum.
Before firing, total momentum \[ = 0 + 0 = 0\]
After firing, total momentum \[ = MV + mv\]
According to the Law of Conservation of Momentum,
\[{\text{MV + mv = 0}}\]
$\Rightarrow MV = - mv \\
\therefore V = - \dfrac{{mv}}{M} $

Therefore, the gun's recoil velocity is \[V = {\text{ - }}\dfrac{{mv}}{{M{\text{ }}}}\] . The negative symbol denotes that the gun is moving in the opposite direction as the bullet.

Note: It should be noted that the installation of shock absorbing suspensions, silencers, and other devices can reduce the recoil of a rifle. Recoil velocity is low because the mass of the bullet shot is modest in comparison to the gun's mass. The recoil is actually caused by the accelerating bullet.