Question

A boy throws a ball upwards with a velocity of $5\text{m/s}$ from a balloon descending with a constant velocity of $15\text{m/s}$. After how much time will the boy be able to catch the ball? Take $g=10{\text{m/s}}^2$ .

• A. $5\text{s}$
• B. $20\text{s}$
• C. $15\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is D $4\text{s}$

Reference direction:
Upwards$\Rightarrow$ $+$ve
Downwards$\Rightarrow$ $-$ve

Therefore, the relative velocity of the ball with respect to the balloon is (solving from balloon frame ):

$u_{rel}=5-(-15)=5+15=20\text{m/s}$

The total displacement of the ball is zero as it returns to the boy again.
$a_{rel}=-g$

Now applying kinematic equation in the relative frame of reference:
$s_{rel}=u_{rel}+\frac{1}{2}{a}_{rel}{t}^2$
$\Rightarrow 0=20t+\frac{1}{2}(-g)t^2$
$20t=\frac{1}{2}\times 10\times t^2$
$\Rightarrow t=4\text{s}$

Hence ,the boy can catch the ball after $4\text{s}$