Question

A balloon was moving upwards with a uniform velocity of $10{\text{ms}}^{-1}$. An object of finite mass is dropped from the balloon when it was at a height of $75\text{m}$ from the ground level. The height of the balloon from the ground when the object strikes the ground will be around :
$(\text{Take}g=10{\text{ms}}^{-2})$

• A. $300\text{m}$
• B. $200\text{m}$
• C. $125\text{m}$
• D. $250\text{m}$

Answer 1

The correct option is C $125\text{m}$


$u=10\text{m/s};a=-g=-10{\text{m/s}}^2;s=-75\text{m}$

Object is projected as shown, so as per equation of motion under gravity,

Time taken by the object to reach the ground is given by,

$s=ut+\frac{1}{2}a{t}^2$

$-75=+10t+\frac{1}{2}(-10)t^2$

Since, $t$ can't be negative

$\therefore t=5\text{s}$

As the balloon is undergoing uniform motion,

Height of balloon from ground when the object reaches the ground is

$H=75+ut$

$\Rightarrow H=75+(10\times 5)=125\text{m}$

Hence, option $\left(\text{C}\right)$ is correct.