A 30-06 caliber hunting rifle fires a bullet of
mass 0.00829 kg with a velocity of 662 m/s to
the right. The rifle has a mass of 3.7 kg.
What is the recoil speed of the rifle as the
bullet leaves the rifle?
662
To find the recoil speed of the rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired should be equal to the total momentum after the bullet is fired.
The total momentum before the bullet is fired can be calculated by multiplying the mass of the bullet by its velocity, and adding it to the product of the mass of the rifle and the velocity of the rifle. Let's call the recoil speed of the rifle "v".
Before the bullet is fired:
Total momentum = (mass of bullet × velocity of bullet) + (mass of rifle × velocity of rifle)
After the bullet is fired:
Total momentum = (mass of rifle × recoil speed of rifle) + (mass of bullet × velocity of bullet)
Since the total momentum before and after the bullet is fired should be the same, we can set up an equation:
(mass of bullet × velocity of bullet) + (mass of rifle × velocity of rifle) = (mass of rifle × recoil speed of rifle) + (mass of bullet × velocity of bullet)
We can simplify this equation by canceling out the terms on both sides that are the same:
mass of rifle × velocity of rifle = mass of rifle × recoil speed of rifle
Now let's solve for the recoil speed of the rifle:
recoil speed of rifle = (mass of rifle × velocity of rifle) / mass of rifle
recoil speed of rifle = velocity of rifle
In the given problem, it is mentioned that the velocity of the bullet is 662 m/s to the right. Since the rifle and the bullet are initially at rest, the velocity of the rifle before the bullet is fired is 0 m/s. Therefore, the recoil speed of the rifle is the same as the velocity of the bullet, which is 662 m/s.