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-
A) Cover a distance of $40m$
B) Have a displacement of $40m$
C) Reach the ground in $4s$
D) Begin to move down just after release

Answer 1

Hint
The balloon is rising up with an acceleration means the velocity of the balloon increases with time in upward direction. When stone is released from a balloon after $8s$, then there is an upward velocity of stone. Then, the starting stone moves upward and then it starts falling downward and falls down to ground.

Complete step by step solution
Balloon is rising with an acceleration of $1.25m{s^{ - 2}}$. After $8s$, velocity of balloon is given by-
$v = 1.25 \times 8 = 10m/s$
and distance travelled is given by-
$s = \dfrac{1}{2}a{t^2} = \dfrac{{1.25 \times 8 \times 8}}{2} = 40m$
When we release stone, its initial velocity is $10m/s$ in upward direction and it is released at height of $40m.$Now, the acceleration of stone is equal to acceleration due to gravity.
Let acceleration due to gravity is $10m{s^{ - 2}}$.
The stone starts moving from a height of $40 meters$ and stops at ground, then its displacement is $40 meters$. Initial velocity is $10m/s$, then the distance travelled by stone in upward direction is $5 meter$ in $1 second$. Now stone is at $45 meter$ above the ground and start falling down, time taken by stone to fall down is given by
$s = \dfrac{1}{2}a{t^2}$, here initial velocity is zero.
$t = \sqrt {\dfrac{{2s}}{a}} = \sqrt {\dfrac{{90}}{{10}}} = \sqrt 9 = 3\operatorname{s}$
Then total time taken is $t + 1 = 4\sec$.
Hence the correct answer is option (B) and (C).

Note
If we have given the value of acceleration due to gravity, then we use the given value otherwise we use $10m{s^{ - 2}}$ or $9.8m{s^{ - 2}}$, according to the given condition in problem. Here the total distance covered by stone is $50 meters$ but displacement is $40 meters$.