Question

Derive recoil velocity.

Answer 1

When a bullet is fired from the gun, due to 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.

The sum of momentum before firing bullet is zero.
mu1+Mu2=0
If v1 and v2 are the final velcoities 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 velocity of the gun is opposite to the direction of velocity of bullet.