A mass `m` moving horizontal (along the x-axis) with velocity `v` collides and stricks to mass of `3m` moving vertically upward (along the y-axis) with velocity `2v`. The final velocity of the combination is

Options

A. `(1)/(4) v hati + (3)/(2) v hatj`
B. `(1)/(3) v hati + (2)/(3) v hatj`
C. `(2)/(3) v hati + (1)/(3) v hatj`
D. `(3)/(2) v hati + (1)/(4) v hatj`

Explanation

To solve the problem of finding the final velocity of the combined mass after the collision, we can follow these steps:

### Step 1: Identify the masses and their velocities
- Mass \( m \) is moving horizontally along the x-axis with velocity \( v \).
- Mass \( 3m \) is moving vertically upward along the y-axis with velocity \( 2v \).

### Step 2: Determine the initial momentum of each mass
- The momentum of mass \( m \) moving along the x-axis is given by:
...