Two balls of masses m and 2m moving in opposite directions collide head on elastically with velocities `v` and `2v`. Find their velocities after collision.

Explanation

To solve the problem of two balls of masses \( m \) and \( 2m \) colliding elastically with initial velocities \( v \) and \( 2v \) in opposite directions, we will use the principles of conservation of momentum and the properties of elastic collisions.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Mass of first ball, \( m_1 = m \) with initial velocity \( u_1 = v \) (moving to the right).
- Mass of second ball, \( m_2 = 2m \) with initial velocity \( u_2 = -2v \) (moving to the left).

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