Question

A man in a hot air balloon, throws a stone downwards with a speed of $5\text{m/s}$ with respect to the balloon. If 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 $2\text{second}$ is
(Take $g=10{\text{m/s}}^2$)

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

Answer 1

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

Let $u$ be the relative velocity of stone with respect to man and $a$ be the relative acceleration of same.

$u=5\text{m/s}$ and
$a=5+g=5+10=15{\text{m/s}}^2$

Now using first equation of motion

$v=u+at$

$\Rightarrow v=5+(15\times 2)=35\text{m/s}$

$\therefore$ relative velocity after $t=2\text{second}$ is $35\text{m/s}$.

$$\begin{array}{c}\text{Why this question?}\\ \text{Acceleration of projectile w.r.t balloon}\\ \text{= Acceleration of projectile w.r.t ground}\\ \text{- Acceleration of balloon w.r.t ground.}\end{array}$$