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Question:

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

14v^i+32v^j

23v^i+13v^j

32v^i+14v^j

13v^i+23v^j

Solution:

From momentum conservation
mv^i + 3m(2v)^j = (4m)→v
→v = v/4^i + 6/4v^j = v/4^i + 3/2v^j