Perpendicular Collision and Sticking Masses – Rankers Physics

Collision: Practice Problem & Solution

A mass $m$ moving horizontally (along the $x$-axis) with velocity $v$ collides and sticks to a mass of $3\text{ m}$ moving vertically upward (along the $y$-axis) with velocity $2v$. The final velocity of the combination is: (2011 Mains)
$\frac{3}{2}\hat{i} + \frac{1}{4}\hat{j}$
$\frac{1}{4}v\hat{i} + \frac{3}{2}v\hat{j}$
$\frac{1}{3}v\hat{i} + \frac{2}{3}v\hat{j}$
$\frac{2}{3}v\hat{i} + \frac{1}{3}v\hat{j}$

Solution Explained:

To solve this problem, we apply the core principles of Collision. Understanding the underlying formula is key to arriving at the correct answer below:

By conservation of momentum, total initial momentum vector is $\vec{P} = mv\hat{i} + (3m)(2v)\hat{j}$. Dividing by the total mass $4m$ gives the final velocity vector $\vec{v}_f = \frac{1}{4}v\hat{i} + \frac{3}{2}v\hat{j}$.

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