Question

From a balloon is moving Upwards with velocity $12m{s}^{-1}$. It releases a packet when it is at a height of $65m$ from the ground. How much time the packet will take to reach the ground $\left(g=10m/se{c}^2\right)$

• A. 5 sec
• B. 6 sec
• C. 7 sec
• D. 8 sec
• E. 10 sec

Answer 1

Answer: (A)

Given, $u=12m{s}^{-1}$
$S=-65m$
$\Rightarrow g=-10m{s}^{-2}$
We know that, $s=ut+\frac{1}{2}g{t}^2$
$\Rightarrow -65=12t-\frac{1}{2}\times 10t^2$
$-65=12t-5t^2$
$\Rightarrow 5t^2-12t-65=0$
$5t^2-25t+13t-65=0$
$5t(t-5)+13(t-5)=0$
$(5t+13)(t-5)=0$
$\Rightarrow t=-\frac{13}{5}s$ or $t=5s$
Time taken by balloon to reach on ground $t=5s$