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 $2\,v$. The final velocity of the combination is

• A. $\frac{3}{4} v \hat {i} + \frac{1}{4} v \hat {j}$
• B. $\frac{1}{4} v \hat {i} + \frac{3}{2} v \hat {j}$
• C. $\frac{1}{3} v \hat {i} + \frac{2}{3} v \hat {j}$
• D. $\frac{2}{3} v \hat {i} + \frac{1}{3} v \hat {j}$

Answer 1

Answer: (B)

From the law of conservation of linear momentum
$mv \,\hat{ i }+(3 m )(2\, v ) \hat{ j } $
$=4 \,mv '$
$v'=\frac{v}{4} \hat{i}+\frac{3}{2} v\hat{j}$