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. `3/2 v hat i + 1/4 v hat j`
B. `1/4 v hat i + 3/2 v hat j`
C. `1/3 v hat i + 2/3 v hat j`
D. `2/3 v hat i + 1/3 v hat j`

Answer

`(2)`

Explanation

Acoording to conservation of momentum, we get `mv hat i + (3m) 2v hat j = (m + 3m )v`
where v. is the final velocity after collision
`v. = 1/4 v hat i + 6/4 v hat j = 1/4 vhat i + 3/2 v hat j`