This is an ”explosion” question.

A 30-06 caliber hunting rifle fires a bullet of
mass 0.0164 kg with a velocity of 254 m/s to
the right. The rifle has a mass of 3.62 kg.
What is the recoil speed of the rifle as the
bullet leaves the rifle?
Answer in units of m/s

.

The recoil speed of the rifle is 0.7 m/s.

To determine 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 leaves the rifle.

The momentum of an object is calculated by multiplying its mass with its velocity. Let's denote the initial velocity of the bullet as Vb, the final velocity of the bullet as Vbf, and the recoil velocity of the rifle as Vr.

Before the bullet is fired, the total momentum is given by:
Initial momentum = (mass of bullet * velocity of bullet) + (mass of rifle * velocity of rifle)

After the bullet leaves the rifle, the total momentum is given by:
Final momentum = (mass of bullet * velocity of bullet after firing) + (mass of rifle * velocity of rifle after firing)

Since the bullet is fired with a velocity of 254 m/s to the right, we can write:
Vb = 254 m/s

As the bullet leaves the rifle, its velocity is zero, so:
Vbf = 0 m/s

Using the principle of conservation of momentum, we can equate the initial and final momenta:
(mass of bullet * Vb) + (mass of rifle * velocity of rifle) = (mass of bullet * Vbf) + (mass of rifle * Vr)

First, let's calculate the initial momentum:
Initial momentum = (0.0164 kg * 254 m/s) + (3.62 kg * velocity of rifle)

Since the bullet has left the rifle and comes to rest, its final momentum is zero. This simplifies the equation to:
(0.0164 kg * 254 m/s) + (3.62 kg * velocity of rifle) = 0

Now, we can solve for the recoil velocity of the rifle (Vr):
3.62 kg * velocity of rifle = - (0.0164 kg * 254 m/s)
velocity of rifle = - (0.0164 kg * 254 m/s) / 3.62 kg

Calculating this equation will give us the recoil velocity of the rifle.

To find the recoil speed of the rifle as the bullet leaves, we can apply the law of conservation of momentum. According to this law, the total momentum before the event should be equal to the total momentum after the event.

The momentum, p, of an object is calculated by multiplying its mass, m, by its velocity, v:

p = m * v

Let's denote the initial velocity of the rifle as Vr and the final velocity of the rifle as Vr'. The mass of the bullet is mb, the mass of the rifle is mr, and the velocity of the bullet is vb. Given values are:

mb = 0.0164 kg
vb = 254 m/s
mr = 3.62 kg

Initially, the total momentum is the sum of the momentum of the bullet and the momentum of the rifle, considering the bullet is moving in the positive direction and the rifle is initially at rest:

Total initial momentum = mb * vb + mr * Vr

After the bullet leaves the rifle, the total momentum is given by the momentum of the rifle alone:

Total final momentum = mr * Vr'

Since momentum is conserved, we can equate the initial and final total momenta:

mb * vb + mr * Vr = mr * Vr'

Now, we can rearrange the equation to solve for Vr':

mr * Vr' = mb * vb + mr * Vr

Dividing both sides of the equation by mr:

Vr' = (mb * vb + mr * Vr) / mr

Plugging in the given values:

Vr' = (0.0164 kg * 254 m/s + 3.62 kg * 0) / 3.62 kg

Simplifying:

Vr' = (4.1856 kg·m/s) / 3.62 kg

Vr' = 1.15569 m/s

Therefore, the recoil speed of the rifle as the bullet leaves the rifle is approximately 1.16 m/s.