Question

A balloon going upward with a velocity of $12m/s$ is at a height of $65m$ from the earth's surface at any instant. Exactly at this instant a ball drops from it. How much time will the ball take in reaching the surface of earth ? $(g=10m/s^2)$

• A. $5s$
• B. $6s$
• C. $10s$
• D. None of these

Answer 1

Answer: (A)

From equation of motion, we have
$h=ut+\frac{1}{2}g{t}^2$
where $u$ is initial velocity, $g$ the acceleration due to gravity and $t$ the time taken.
Taking upward direction as negative and downward direction as positive, we have
$h=65m$,
$u=-12m/s,g=10m/s^2$

$\therefore 65=-12t+\frac{1}{2}\times 10\times t^2$
$\therefore 5t^2-12t-65=0$
$\Rightarrow (t-5)(5t+13)=0$
$\therefore t=5s$