# Formula for Recoil Velocity of the Gun

The mass of the ejected body and the mass of the recoiling body are related to one another by the law of conservation of momentum which is obtained from Newton’s laws of motion.

According to the law of conservation of momentum, for every action, there is an equal and opposite reaction. Recoiling velocity is an example of this law. From the law, it can be said that

m1v1 = -m2v2

Where,

m1 and v1 are the mass and velocity of the bullet

m2 and v2 are the mass and velocity of the gun

We know that recoil velocity is the velocity of a body after the ejection of the object from the body. Therefore, following is the recoil velocity of the gun:

 $$\begin{array}{l}v_{2}=-(frac{m_{1}}{m_{2}})v_{1}\end{array}$$