A balloon starts rising from the ground with an acceleration of 1… - Vidyadip

MCQ

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

A
Cover a distance of $40m.$
B
Have displacement of $50m.$
✓
Reach the ground in $4$ second.
D
Begin to move downward after being released.

✓

Answer

Correct option: C.

Reach the ground in $4$ second.

Taking upward motion of balloon for $8$ seconds; we have
$u = 0; a = 1.25\ m/s^2; t = 8 s; v = ?; s = ?.$
Here $v = u + at = 0 + 1.25 \times 8 = 10\ m/s$
$\text{s}=\text{ut}+\frac{1}{2}\text{at}^2$
$=0+\frac{1}{2}\times1.25\times8^2=40\text{m}$
Taking downward motion of released stone from balloon at height $40m$ we have,
$a = -10\ m/s; a = 10\ m/s^2; s = 40m; t = ?$
As, $\text{s}=\text{ut}+\frac{1}{2}\text{at}^2$
so, $40=-10\text{t}+\frac{1}{2}\times10\times\text{t}^2$
or $t^2 - 2t - 8 = 0$ On solving $t = 4s.$

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