A bullet with mass 60.0 g is fired with an initial velocity of 575 m/s from a gun with

mass 4.50 kg. What is the speed of the recoil of the gun?

you didn't convert G into KG, so the answer would be 7.67m/s

(massbullet * velocitybullet)/massgun

(60.0 * 575/4.50) = 7666.66666
Which rounded off becomes 76.7m/s

Ah, the classic case of "bullet vs gun," a tale as old as time. Now, let's break it down with a touch of humor.

To find the speed of the recoil, we'll have to embrace our physics cap. Don't worry, I'll guide you through this scientific circus.

First, let's consider the conservation of momentum. The momentum before the firing should be equal to the momentum after, just like balancing on a unicycle.

The momentum of the bullet can be calculated by multiplying its mass (60.0 g or 0.060 kg) by its velocity (575 m/s). Simple, right?

Now, let's move onto the gun. The mass of the gun is 4.50 kg, and since it's an equal and opposite reaction game, we need to find the speed of its recoil, which we'll call "V."

Using a touch of mathematical magic, we can equate the total momentum before and after the shot like so: (mass of bullet x velocity of bullet) = (mass of gun x velocity of gun recoil).

Plug in the numbers, and you'll find yourself with 0.060 kg x 575 m/s = 4.50 kg x V.

A few calculations later, divide both sides by 4.50 kg, and you'll discover the speed of the recoil, which in this case is 7.0 m/s.

So, after all the math juggling, the speed of the gun's recoil is about 7.0 m/s. Remember, it's all about momentum, balance, and bringing a touch of humor to science. Keep on clowning around!

To find the speed of the recoil of the gun, we can use the principle of conservation of momentum.

According to the principle of conservation of momentum, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.

The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of the bullet as m1, the velocity of the bullet as v1, the mass of the gun as m2, and the velocity of the gun as v2.

Before the bullet is fired:
Momentum of the bullet (m1v1) + Momentum of the gun (m2v2) = 0 (since the gun is at rest)

After the bullet is fired:
Momentum of the bullet (m1v1') + Momentum of the gun (m2v2') = 0 (since the bullet and gun move in opposite directions)

We are given:
m1 = 60.0 g = 0.060 kg (convert grams to kilograms)
v1 = 575 m/s
m2 = 4.50 kg
v2' (speed of the gun recoil) = ?

Using the conservation of momentum equation, we can write:
m1v1 + m2v2 = m1v1' + m2v2'

Substituting the given values:
(0.060 kg)(575 m/s) + (4.50 kg)(0) = (0.060 kg)(v1') + (4.50 kg)(v2')

Simplifying the equation:
0.060 kg * 575 m/s = 0.060 kg * v1' + 4.50 kg * v2'
34.5 kg·m/s = 0.060 kg·v1' + 4.50 kg·v2'

Since the gun is at rest initially (v2 = 0), the equation becomes:
34.5 kg·m/s = 0.060 kg·v1' + 4.50 kg·v2'

Solving for v2':
0.060 kg·v1' = 34.5 kg·m/s
v1' = 34.5 kg·m/s / 0.060 kg
v1' = 575 m/s

Therefore, the speed of the recoil of the gun is 575 m/s.

To find the speed of the recoil of the gun, we can use the principle of conservation of momentum. According to this principle, the momentum before the firing of the bullet is equal to the momentum after the firing.

Momentum is given by the equation: momentum = mass × velocity.

Before the firing, the momentum of the system (bullet + gun) is zero because neither the bullet nor the gun is moving. Therefore, the momentum after the firing must also be zero to satisfy the conservation of momentum.

Let's represent the velocity of the recoil of the gun as Vg and the velocity of the bullet as Vb.

We can set up an equation based on the conservation of momentum:

(Initial momentum) = (Final momentum)

The initial momentum is the momentum of the bullet, and the final momentum is the combined momentum of the bullet and the gun recoil.
Since the bullet is moving in the opposite direction to the recoil of the gun, we need to assign a negative sign to the momentum of the bullet.

Therefore, the equation becomes:

(-Mass of the bullet × Velocity of the bullet) = (Mass of the gun × Velocity of the gun recoil)

Rearranging the equation, we have:

Mass of the gun × Velocity of the gun recoil = -Mass of the bullet × Velocity of the bullet

Now, let's substitute the given values into the equation:

(4.50 kg × Vg) = (-0.060 kg × 575 m/s)

Dividing both sides of the equation by the mass of the gun (4.50 kg), we have:

Vg = (-0.060 kg × 575 m/s) / (4.50 kg)

Calculating the result, we find:

Vg = -0.767 m/s

Since speed is a scalar value, it does not have a direction. Therefore, the speed of the recoil of the gun is 0.767 m/s.