A 30-06 caliber hunting rifle fires a bullet of

mass 0.0101 kg with a velocity of 279 m/s to
the right. The rifle has a mass of 3.46 kg.
What is the recoil speed of the rifle as the
bullet leaves the rifle?
Answer in units of m/s.

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

The initial momentum of the system (rifle and bullet combined) is the sum of the momentum of the rifle and the momentum of the bullet. Since the bullet is fired to the right, its momentum is given by:

Momentum of the bullet = Mass of the bullet * Velocity of the bullet

P_bullet = (0.0101 kg) * (279 m/s) = 2.7999 kg·m/s

The initial momentum of the rifle is the product of the mass of the rifle and its initial velocity, which we need to find:

P_rifle = Mass of the rifle * Initial velocity of the rifle

We know the mass of the rifle is 3.46 kg, and we need to find the initial velocity of the rifle. Since the rifle starts at rest, its initial velocity is 0 m/s.

P_rifle = (3.46 kg) * (0 m/s) = 0 kg·m/s

To find the final momentum of the system, we add the momentum of the rifle and the momentum of the bullet after the bullet is fired. Let's assume the recoil speed of the rifle is v_recoil:

P_f = (Mass of the rifle + Mass of the bullet) * v_recoil

P_f = (3.46 kg + 0.0101 kg) * v_recoil
= 3.4701 kg * v_recoil

According to the conservation of momentum principle, the initial momentum should be equal to the final momentum:

P_f = P_rifle + P_bullet

3.4701 kg * v_recoil = 0 kg·m/s + 2.7999 kg·m/s

This simplifies to:

3.4701 kg * v_recoil = 2.7999 kg·m/s

Next, rearrange the equation to solve for v_recoil:

v_recoil = 2.7999 kg·m/s / 3.4701 kg

Finally, calculate the value:

v_recoil ≈ 0.805 m/s

Therefore, the recoil speed of the rifle as the bullet leaves is approximately 0.805 m/s.