a 2.5 kg rifle fires a 20 g bullet at 400 m/s. What is the magnitude of the recoil velocity of the rifle?

To find the magnitude of the recoil velocity of the rifle, we can use the conservation of momentum principle. According to this principle, the total momentum before the bullet is fired must equal the total momentum after the bullet is fired.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v). Mathematically, momentum can be expressed as:

p = m * v

Given that the rifle has a mass of 2.5 kg and fires a bullet with a mass of 20 g (or 0.02 kg) at a velocity of 400 m/s, we can calculate the initial momentum of the bullet and rifle system before firing:

Initial momentum = (mass of rifle) * (velocity of rifle) + (mass of bullet) * (velocity of bullet)

Initial momentum = (2.5 kg) * (0 m/s) + (0.02 kg) * (0 m/s)

Since the rifle is initially at rest, the velocity of the rifle is 0 m/s.

The bullet's initial momentum is therefore:

Initial momentum = (0.02 kg) * (400 m/s)

Next, let's assume the final recoil velocity of the rifle is V (which is what we are trying to find). The bullet's final velocity is typically much larger than the recoil velocity, so we neglect the bullet's recoil.

According to the conservation of momentum principle:

Initial momentum = Final momentum

(0.02 kg) * (400 m/s) = (2.5 kg + 0.02 kg) * V

Simplifying the equation:

8 kg·m/s = (2.52 kg) * V

Dividing both sides of the equation by (2.52 kg):

V = 8 kg·m/s / 2.52 kg

V ≈ 3.17 m/s

Therefore, the magnitude of the recoil velocity of the rifle is approximately 3.17 m/s.