A body of mass `m _ 1 ` moving with an unknown velocity of ` v _ 1 hati ` , undergoes a collinear collision with a body of mass ` m _ 2 ` moving with a velocity ` v _ 2 hati `. After collision ` m _ 1 and m _ 2 ` move with velocities of ` v _ 3 hati and v _ 4 hati , ` respectively. If ` m _ 2 = 0.5 m _ 1 and v _ 3 = 0.5 v _ 1` , then ` v _ 1 ` is

Explanation

To solve the problem, we need to apply the principle of conservation of linear momentum. The equation for momentum before and after the collision can be set up as follows:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Mass of body 1: \( m_1 \)
- Mass of body 2: \( m_2 = 0.5 m_1 \)
- Initial velocity of body 1: \( v_1 \)
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