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Question

A balloon starts rising from ground from rest with an upward acceleration 2 m/s2. Just after 1 s, a stone is dropped from it. The time taken by stone to strike the ground is nearly

A
0.3 s
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B
0.7 s
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C
1 s
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D
1.4 s
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Solution

The correct option is B 0.7 s
When the stone is dropped from the balloon, its initial velocity is the same as the velocity of the balloon at that instant.
The upward acceleration of the balloon is a=2m/s2
The balloon starts from rest, so u= 0 m/s
The balloon rises for 1 s before the stone is dropped, hence we have
v =u + at
v=0+=2 m/s in the vertically upw ard direction.
This is the initial velocity of the stone after being dropped.

The distance moved up by the balloon in 1 second is
v2=u2+2as
v2=2as
S=v22a=44=1m
Hence, the stone falls by 1 m before hitting the ground

Now, the acceleration on the stone after being dropped is g=9.8m/s2
Hence, for the stone,
we have
u=2m/s;s=1m;a=9.8m/s2;t=1s

u is negative as it is in the upward direction

Hence, using third equation of motion,
we get time as
s=ut+12at2
1=2t+12×9.8t2
4.9t22t1=0
=t=2+(2)24×4.9×(1)2×9.8=2+4+19.62×9.8=2+23.69.8

Since, time cannot be negative, we have
t=2+23.69.8=0.7s

Hence, the stone will strike the ground 0.7 s after being dropped from the balloon.
hence (B) option is correct

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