Question

What is recoil velocity of a gun? How can you derive the expression for recoil velocity of gun?

Answer 1

When a bullet is fired from the gun, due to the reaction force, the gun recoils in the direction opposite to the motion of bullet. The velocity with which it recoils is called as Recoil Velocity.

Derivation For recoil velocity of Gun:

The initial velocity of gun and bullet are at rest.
Hence u1 and u2 =0
let m and M be the mass of bullet and gun respectively.
The sum of momentum before firing bullet is zero.
mu1+Mu2=0If v1 and v2 are the final velocities of bullet and gun receptively after firing.
Then According to law of conservation of momentum
Total momentum before recoil = Total momentum after recoil.
0=mv1+Mv2
Therefore,
Mv2=-mV1V2
= -mV1/M
This the recoil velocity of Gun.
Here negative sign indicates that the direction of the velocity of the gun is opposite to the direction of velocity of the bullet.