Question

A balloon starts rising from the ground with an acceleration of $1.25m/s^2$. After $8s$, a stone is released from the balloon. The stone will (Taking $g=10m/s^2$)

• A. begin to move down after being released
• B. reach the ground in $4$ $s$
• C. cover a distance of $40$ $m$ in reaching the ground
• D. will have a displacement of $50$ $m$

Answer 1

The correct option is B reach the ground in $4$ $s$

$v=1.25\ast 8m/s=10m/s$
$s=\frac{1}{2}\ast 1.25\ast 8\ast 8m/s=40m$

now, $40=-10t+\frac{1}{2}\ast 10\ast t^2$
or, $5t^2-10t-40=0$
or,$t^2-2t-8=0$

hence, $t=4s$

So B is correct.
s$=$40m.

displacement$=$ 40m.

Just after being released the stone has an upward velocity, so it will move upwards first. So A is wrong.
distance in an upward direction before stopping d.

$d=\frac{v^2-u^2}{2g}=\frac{{10}^2-0^2}{2\ast 10}=5m$

and distance$=$ s+2d$=$50m
So the distance covered is 50 m and the displacement is 40 m. So C and D are wrong.