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

Options

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

Answer

B

Explanation

According to conservation of momentum, we get
`m v hati + (3m) 2v hatj = (m + 3 m)v.`
where `v.` is the final velocity after collision
`v. = 1/4 v hati + 6/4 v hatj = 1/4 v hati + 3/2 v hatj` .