Question

A stone is dropped from a balloon at an altitude of $280m$. If the balloon ascends with a velocity of $5m{s}^{-1}$ and descends with a velocity of $5m{s}^{-1}$, times taken by the stone to reach the ground in the two cases respectively are ($g=10m{s}^{-2}$):

• A. $8s$ and $9s$
• B. $9s$ and $8s$
• C. $3s$ and $4s$
• D. $8s$ and $7s$

Answer 1

Answer: (D)

$8s$ and $7s$

Initial speed of the particle becomes same as the ballon have.

Assume upward direction as positive and downward direction as negative.

$1^{st}$ Case:

Ascend with $5m/s$
$u=5m/s$ : Initial velocity of particle

Apply second equation of motion.
$s=ut-\frac{1}{2}g{t}^2$

$\Rightarrow s=5t-5t^2$

Displacement is $-280m$, in downward direction

$\Rightarrow 5t-5t^2=-280$
$\Rightarrow t=8sec$

$2^{nd}$ Case:

Descend with $5m/s$

$u=-5m/s$ : Initial velocity of particle

Apply second equation of motion.
$s=ut-\frac{1}{2}g{t}^2$

Displacement is $-280m$, in downward direction

$\Rightarrow -280=-5t-5t^2$

$\Rightarrow t=7sec$