Question

A man in a ballon, throws a stone downwards with a speed of $5\text{m/s}$ with respect to ballon. The balloon is moving upwards with a constant acceleration of $5{\text{m/s}}^2$. Then the velocity of the stone relative to the man after $2\text{sec}$ is (take $g=10{\text{m/sec}}^2$):

• 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 $35\text{m/s}$

Given,

Relative velocity of stone w.r.t balloon $u=$ $5\text{m/s}$ (downward),

Acceleration of the balloon, $a=5{\text{m/sec}}^2$

Relative accelaration of stone w.r.t. balloon, $=g-(-a)=10-(-5)=15{\text{m/s}}^2$ (downward)

So, the velocity of the stone relative to the man after $2\text{sec}$ is ,

$v=u+at=5+15\times 2=35\text{m/s}$

Hence, option (a) is correct answer.

Why this question ? To make the student familiar with the concept of relative acceleration.