A machine gun with a man of 4kg fires a 45g bullet at a speed 100m/s . Find the recoil speed of the machine gun?

To find the recoil speed of the machine gun, we can use the principle of conservation of momentum.

The momentum of the man and the bullet before firing is zero, as they are at rest. After firing, the total momentum of the man and the bullet must still be zero.

Let the recoil speed of the machine gun be v.

The momentum of the man and the bullet after firing is given by:

(4kg + 0.045kg) * v = 4kg * (-100m/s) + 0.045kg * (100m/s)

4.045kg * v = -400kgm/s + 4.5kgm/s
4.045kg * v = -395.5kgm/s
v = -395.5kgm/s / 4.045kg
v = -97.9m/s

Therefore, the recoil speed of the machine gun is 97.9m/s in the opposite direction of the bullet.