A bullet of mass 50 g is fired from a gun with initial velocity of 35 m/s. If mass of the gun is 4 kg, then calculate the recoil velocity of the gun.

Explanation

To solve the problem of calculating the recoil velocity of the gun when a bullet is fired, we will use the principle of conservation of linear momentum. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a bullet of mass \( m_2 = 50 \, \text{g} = 0.05 \, \text{kg} \) fired from a gun of mass \( m_1 = 4 \, \text{kg} \) with an initial velocity \( v_2 = 35 \, \text{m/s} \). We need to find the recoil velocity \( v_1 \) of the gun.

### Step 2: Apply Conservation of Linear Momentum
According to the law of conservation of momentum:
\[
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