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 can apply the principle of conservation of 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 of the gun, which we will denote as \( v_1 \).

### Step 2: Apply Conservation of Momentum
According to the law of conservation of momentum, the total momentum before firing must equal the total momentum after firing. Initially, both the gun and bullet are at rest, so the total initial momentum is zero.

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