From a rifle of mass $4kg$, a bullet of mass $50g$ is fired with an initial velocity of $35m{s}^{-1}$. Calculate the initial recoil velocity of the rifle.

Step 1: Given Information:

Mass of rifle, $M=4kg$

Mass of bullet, $m=50g$

Initial velocity of bullet, $v=35m{s}^{-1}$

Step 2: To find

Initial recoil velocity

Step 3: Formula and solution

According to law of conservation of momentum,

total momentum before collision = total momentum after collision

Before firing, the velocity of gun and bullet is zero, so

$$\begin{gathered} 0=MV+mv \\ \Rightarrow MV=-mv \\ \Rightarrow V=\frac{-mv}{M} \\ \Rightarrow V=\frac{-50\times 35}{4\times 1000} \\ \Rightarrow V=\frac{-7}{16} \\ \Rightarrow V=-0.4375m{s}^{-1} \end{gathered}$$

The recoil velocity of the gun is $-0.4365m{s}^{-1}$. The negative sign shows that the recoil velocity will act opposite to the direction of motion of the bullet.