From a rifle of mass 4kg, a bullet of mass 50 g is fired with an initial velocity of 35m/s. Calculate the initial recoil velocity of the rifle.

The initial recoil velocity of the rifle is $-0.44m/s$.
Given,
Mass of the rifle, $\mathit{M }= 4\mathit{ kg}$.
Bullet’s mass,$m=50\mathit{ g}$.
⇒ $m=0.05\mathit{ kg}$
The Initial velocity of the bullet,$\mathit{u }= 35\mathit{ m}/s$.
Assume, the recoil speed of the rifle is $v\mathit{ }m\mathit{/}s$.
At the time of the fire, the bullet and rifle were at rest so their momentum was zero.
After the fire,
The momentum of the bullet $=\mathit{ mu}$
The momentum of the rifle$=\mathit{ Mv}$
Total momentum$=\mathit{ Mv}+\mathit{mu}$
There exists no external force, so, the momentum before and after the fire is the same.
⇒ $\mathit{Mv}+\mathit{mu}=0$
⇒  $\mathit{Mv}=-\mathit{mu}$
⇒  $v=\frac{-\mathit{mu}}{M}$
⇒ $v=\frac{-0.05\mathit{ kg}\times 35\mathit{ m}\mathit{/}s}{4\mathit{ kg}}$
⇒  $v=-0.44\mathit{ m}/\mathit{s }$
A negative sign shows that the direction of the recoil velocity is opposite to the velocity of the bullet.