A 75.0g bullet is fired at a muzzle velocity of 476 m/s from a gun with a mass of 4.75kg and a barrel length of 60.0cm.

a. How long is the bullet in the barrel?

b. What is the force of the bullet while it is in the barrel?

c. Find the impulse given to the bullet while it is in the barrel.

d. Find the bullet's momentum as it leaves the barrel.

To answer these questions, we can use the principles of physics related to projectiles, forces, and momentum. Let's break down each part of the problem step by step:

a. How long is the bullet in the barrel?

To calculate the time the bullet spends in the barrel, we need to use the equation of motion:

vf = vi + at

Where:
- vf is the final velocity (which is zero since the bullet stops when it leaves the barrel)
- vi is the initial velocity (which is the muzzle velocity of 476 m/s)
- a is the acceleration (which we need to find)
- t is the time (which we need to find)

The acceleration is given by Newton's second law: F = ma, where F is the force.

b. What is the force of the bullet while it is in the barrel?

To calculate the force, we need to use Newton's second law:

F = ma

Where:
- F is the force (which we need to find)
- m is the mass of the bullet (given as 75.0 g)
- a is the acceleration (which we need to find)

c. Find the impulse given to the bullet while it is in the barrel.

Impulse (J) is defined as the change in momentum. We can calculate impulse using the formula:

J = Δp = mΔv

Where:
- J is the impulse (which we need to find)
- Δp is the change in momentum
- m is the mass of the bullet (given as 75.0 g)
- Δv is the change in velocity (initial velocity minus final velocity)

d. Find the bullet's momentum as it leaves the barrel.

Momentum (p) is defined as the product of an object's mass and its velocity. We can calculate momentum using the formula:

p = mv

Where:
- p is the momentum (which we need to find)
- m is the mass of the bullet (given as 75.0 g)
- v is the velocity of the bullet (which we consider to be the muzzle velocity of 476 m/s)

Now, let's apply these formulas and solve the problem.

a. To find the time the bullet is in the barrel, we need to find the acceleration first. Since the bullet stops when it leaves the barrel, the final velocity is zero. Using the equation vf = vi + at, we can rearrange it to solve for acceleration:

0 = 476 m/s + a * t

Since the bullet starts from rest (vi = 0), the equation becomes:

a * t = -476 m/s

We have a = F / m, where F is the force and m is the mass of the gun. And we know that m = 4.75 kg. Therefore, the equation becomes:

(4.75 kg) * t = -476 m/s

From this equation, we can solve for t by dividing both sides by 4.75 kg:

t = -476 m/s / 4.75 kg

Now we can calculate the time the bullet is in the barrel.

b. To find the force of the bullet, we use the equation F = ma. We know that m = 75.0 g, but it needs to be converted to kilograms (1 kg = 1000 g). Therefore, m = 75.0 g / 1000 g/kg. We also know that acceleration can be found using the equation a = F / m. Rearranging this equation will give us F = a * m. So, we can substitute the values into the formula to calculate the force of the bullet.

c. To find the impulse given to the bullet while it is in the barrel, we use the formula J = mΔv.Δv is the change in velocity, which is the final velocity minus the initial velocity. In this case, the initial velocity is the muzzle velocity, and the final velocity is zero.

d. To find the bullet's momentum as it leaves the barrel, we use the formula p = mv. We know the mass of the bullet and the muzzle velocity, so we can substitute those values into the formula to calculate its momentum.