A machine gun with a mass 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 bullet before firing is given by:
Initial momentum = mass x velocity
Initial momentum = 0.045kg x 100m/s
Initial momentum = 4.5 kg m/s

According to the conservation of momentum, the total momentum before firing is equal to the total momentum after firing. Therefore, the momentum of the machine gun and the bullet after firing should be equal to the initial momentum.

Let the recoil speed of the machine gun be v m/s. The momentum of the machine gun and the bullet after firing is given by:
Final momentum = (mass of bullet + mass of machine gun) x recoil speed
Final momentum = (0.045kg + 4kg) x v
Final momentum = 4.045kg x v

Since the total momentum before firing is equal to the total momentum after firing, we have:
Initial momentum = Final momentum
4.5 kg m/s = 4.045kg x v

Solving for v, we get:
v = 4.5 kg m/s / 4.045kg
v = 1.113 m/s

Therefore, the recoil speed of the machine gun is 1.113 m/s.