Question

A stone is dropped from a balloon going up with a uniform velocity of $5\text{m/s}.$ If the balloon was $60\text{m}$ high when the stone was dropped, find the height of balloon when the stone hits the ground. Take $g=10\text{m/s}$.

• A. $50\text{m}$
• B. $60\text{m}$
• C. $80\text{m}$
• D. $100\text{m}$

Answer 1

The correct option is C $80\text{m}$


Time taken by the stone to reach the ground:
$s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow -60=5\left(t\right)+\frac{1}{2}(-10)t^2$
$\Rightarrow -60=5t-5t^2$
$\Rightarrow 5t^2-5t-60=0$
$\Rightarrow t^2-t-12=0$
$\Rightarrow t^2-4t+3t-12=0$
$\Rightarrow (t-4)(t+3)=0$
$\Rightarrow t=4s$
Height of balloon from ground at this instant is
$h=60+\left(4\right)\left(5\right)$
$\Rightarrow h=80\text{m}$