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

$1 half straight v space bold i with bold hat on top space plus 3 over 2 straight v space bold j with bold hat on top$
$1 third straight v space bold i with bold hat on top space plus 2 over 3 straight v space bold j with bold hat on top$
$2 over 3 straight v space bold i with bold hat on top space plus 1 third straight v space bold j with bold hat on top$
$3 over 2 straight v space bold i with bold hat on top space plus 1 fourth straight v space bold j with bold hat on top$

Solution

1 half straight v space bold i with bold hat on top space plus 3 over 2 straight v space bold j with bold hat on top

From the law of conservation of linear momentum

mv + (3m)(2v) = (4m)v'
mv i + 6mv j = 4 mv'

$straight v apostrophe space equals space 1 fourth space straight v space bold i space plus space 6 over 4 space straight v space bold j straight v apostrophe space equals space 1 fourth space straight v space bold i bold space plus 3 over 2 space straight v space bold j$