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Question

A stone is dropped from a balloon at an altitude of 280 m. If the balloon ascends with a velocity of 5 ms−1 and descends with a velocity of 5 ms−1, times taken by the stone to reach the ground in the two cases respectively are (g=10 ms−2):

A
8 s and 9 s
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B
9 s and 8 s
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C
3 s and 4 s
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D
8 s and 7 s
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Solution

The correct option is C 8 s and 7 s
Initial speed of the particle becomes same as the ballon have.
Assume upward direction as positive and downward direction as negative.
1st Case:
Ascend with 5 m/s
u=5 m/s : Initial velocity of particle
Apply second equation of motion.
s=ut12gt2
s=5t5t2
Displacement is 280 m, in downward direction
5t5t2=280
t=8 sec
2nd Case:
Descend with 5 m/s
u=5 m/s : Initial velocity of particle
Apply second equation of motion.
s=ut12gt2
Displacement is 280 m, in downward direction
280=5t5t2
t=7 sec

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