Question

A balloon starts rising from the ground with an acceleration of $1.25m/s^2$. After 8 seconds, a stone is released from the balloon. After releasing, the stone will

• A. cover a distance of 40 m till it strikes the ground.
• B. have a displacement of 50 m till it reaches the ground
• C. reach the ground in 4 seconds.
• D. begin to move down instantaneously

Answer 1

The correct option is C reach the ground in 4 seconds.

The velocity of balloon at time $t=8$sec

$v=u+at$

Initial velocity$=u=0$

Acceleration$=a=1.25㎧$

$\therefore v=at$

$=1.25\times 8$

$v=10㎧$

To find distance

$2as=v^2-u^2$

$\therefore S=\frac{v^2-u^2}{2a}$

$=\frac{100}{2\times 1.25}$

$\therefore S=40m$

After stone release it will cover same distance in opposite direction

$\therefore S=-40m$

Free fall of motion

$\therefore S=ut-\frac{1}{2}g{t}^2$

$-40=10t-5t^2$

On solving we get two values of t

$t=-2$ and $t=4$

Time cannot be negative

$\therefore$ stone will reach the gound in $4$ sec