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Question

# A hot air balloon is rising vertically upwards at a constant velocity of 10 msâˆ’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 msâˆ’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 mVelocity 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 ms−1, i.e. u=+10 ms−1. Also g=−10 ms−2 (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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