A 60 g bullet fired from a 5 kg gun leaves with a speed of 500 m/s. Find the speed (velocity) with which the gun recoils (jerks backwards).

Answer

To find the speed (velocity) with which the gun recoils when a bullet is fired, we can use the principle of conservation of momentum. Here's how to solve the problem step by step:

### Step 1: Understand the Given Data
- Mass of the bullet (m1) = 60 g = 0.06 kg (since 1 g = 0.001 kg)
- Velocity of the bullet (v1) = 500 m/s
- Mass of the gun (m2) = 5 kg
- Recoil velocity of the gun (v2) = ?

### Step 2: Apply the Law of Conservation of Momentum
According to the law of conservation of momentum, the total momentum before the firing of the bullet is equal to the total momentum after the bullet is fired.

Before firing:
- Total momentum = 0 (since both the bullet and gun are at rest)

After firing:
- Momentum of the bullet = m1 * v1
- Momentum of the gun = m2 * v2

Thus, we can write the equation:
\[ m1 \cdot v1 + m2 \cdot v2 = 0 \]

### Step 3: Rearrange the Equation
Since the gun recoils in the opposite direction of the bullet, we can express the momentum of the gun as negative:
\[ m1 \cdot v1 = -m2 \cdot v2 \]

### Step 4: Solve for v2
Now, we can rearrange the equation to solve for the recoil velocity of the gun (v2):
\[ v2 = -\frac{m1 \cdot v1}{m2} \]

### Step 5: Substitute the Values
Now, substitute the known values into the equation:
\[ v2 = -\frac{0.06 \, \text{kg} \cdot 500 \, \text{m/s}}{5 \, \text{kg}} \]

### Step 6: Calculate v2
Calculating the above expression:
\[ v2 = -\frac{30}{5} = -6 \, \text{m/s} \]

The negative sign indicates that the gun recoils in the opposite direction to the bullet.

### Final Answer
The speed (velocity) with which the gun recoils is **6 m/s** backward.

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