2.5 kg rifle fires a 20 g bullet at 400 m/s.

Find magnitude of the recoil velocity of the rifle.

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

The momentum of an object is given by the product of its mass and velocity. So, we can calculate the momentum of the bullet and the rifle before and after the bullet is fired.

Before the bullet is fired:
The momentum of the bullet and the rifle combined is zero because they are initially at rest. So the total momentum before the bullet is fired is:

momentum_before = (mass_of_rifle + mass_of_bullet) * velocity_before

Given:
mass_of_rifle = 2.5 kg
mass_of_bullet = 20 g = 0.02 kg
velocity_before = 0 m/s (initially at rest)

So, the momentum before the bullet is fired is zero.

After the bullet is fired:
The momentum of the bullet is given by the product of its mass and velocity:

momentum_of_bullet = mass_of_bullet * velocity_of_bullet

Given:
mass_of_bullet = 0.02 kg
velocity_of_bullet = 400 m/s

So, the momentum of the bullet after it is fired is:

momentum_of_bullet = 0.02 kg * 400 m/s = 8 kg·m/s

According to the principle of conservation of momentum, the total momentum after the bullet is fired should be equal to the total momentum before the bullet was fired. Since the momentum before the bullet was fired is zero, the momentum after the bullet is fired should also be zero.

So, the recoil velocity of the rifle can be calculated using the equation:

momentum_of_rifle * velocity_of_rifle = 0

Since momentum_of_rifle = -momentum_of_bullet (to maintain conservation of momentum)

velocity_of_rifle = -momentum_of_bullet / mass_of_rifle

Substituting the known values:

velocity_of_rifle = -8 kg·m/s / 2.5 kg = -3.2 m/s

The magnitude of the recoil velocity of the rifle is the absolute value of the result:

magnitude_of_recoil_velocity = |velocity_of_rifle| = 3.2 m/s

So, the magnitude of the recoil velocity of the rifle is 3.2 m/s.

See the answers to the same related question listed below.

This is a conservation of momentum problem.

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