The correct option is
B 0.7 sWhen 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
4.9t2−2t−1=0
∴=t=2+−√(−2)2−4×4.9×(−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