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Question

A hot air balloon is rising vertically upwards at a constant velocity of 10 ms−1. When it is at a height of 45 m from the ground, a man bails out from it. After 3 s he opens his parachute and decelerates at a constant rate of 5 ms−2. How far is parachutist from the balloon at t=3 s?

A
15 m
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B
30 m
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C
45 m
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D
60 m
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Solution

The correct option is C 45 m
Velocity of balloon =+10 m/s (as the velocity of the balloon is upwards)
When the parachutist bails out, he has the velocity of the balloon and has an upward velocity of 10 ms1, i.e. u=+10 ms1.
Also g=10 ms2 (acting downwards).
The displacement of parachutist in t=3 s is given by
S=ut+12gt2 (By second equation of motion)
=10×3+12×(10)×(3)2
=15 m
Since the displacement is negative, it is directed downwards.
The height by which balloon will rise in time (t=3 s)=10×3=30 m
We know that, the displacement of parachutist in 3 s=15 m.
Hence, the parachutist is now 30(15)=45 m away from the balloon.
Thus, the correct choice is (c).

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