A bullet with a mass of 50kg leaves the barrel of a rifle wiyh a velocity of 400m.-1 ,if the mass of the rifle is 3kg ,what is the recoil velocity of the rifle?

To find the recoil velocity of the rifle, we can apply the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.

The equation for momentum is given by:

Momentum = Mass × Velocity

Let's denote the bullet's mass as m1, the bullet's velocity as v1, the rifle's mass as m2, and the recoil velocity of the rifle as v2.

The total momentum before the bullet is fired is:

Initial momentum = (m1 + m2) × 0
= 0

The total momentum after the bullet is fired is:

Final momentum = (m1 × v1) + (m2 × v2)

According to the law of conservation of momentum, the total momentum before and after the event must be equal. Therefore, we can write:

0 = (m1 × v1) + (m2 × v2)

Rearranging the equation to solve for v2, the recoil velocity of the rifle:

v2 = -((m1 × v1) / m2)

Now, let's substitute the known values into the equation:

m1 = 50 kg (mass of the bullet)
v1 = 400 m/s (velocity of the bullet)
m2 = 3 kg (mass of the rifle)

v2 = -((50 kg × 400 m/s) / 3 kg)

By calculating this expression, we can find the recoil velocity of the rifle.