Question

A man in a balloon, throws a stone downwards with a speed of $5\text{m/s}$ with respect to the balloon. The balloon is moving upwards with a constant acceleration of $5{\text{m/s}}^2.$ Then velocity of the stone relative to the man after $2\text{seconds}$ is:

• A. $10\text{m/s}$
• B. $30\text{m/s}$
• C. $15\text{m/s}$
• D. $35\text{m/s}$

Answer 1

The correct option is D $35\text{m/s}$

In a frame relative to balloon,
${\overrightarrow{u}}_{SB}=5\text{m/sec}(-\hat{j})$
${\overrightarrow{a}}_{SB}=15{\text{m/sec}}^2(-\hat{j})$
$\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t$
$\overrightarrow{v}=-5-15\times 2\left(\hat{j}\right)=-35\text{m/sec}\left(\hat{j}\right)$
$|\overrightarrow{v}|=35\text{m/s}$