Question

A body is dropped from a balloon which is moving upward with a speed of 10m/s.The body is dropped when the balloon is at a height of 390m from the surface of earth.Find the approximate time taken by the body to reach the surface of earth.Take g=10m/s2.

Answer 1

the baloon is moving upward with velocity 10ms-1 so the body will also move with upward velocity 10ms-1
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refer pic.
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in addition to th √79 s there will be no more second which the body have taken to reach the highest points so the answer will be 1 +√79

Answer 2

First, we write all the known quantities 
a= -10m's^2
s= 390 m
u= +10m/s
s=ut + 1/2at^2
s=10t + 5t^2
-390=10t + 5t^2
-78= 2t - t^2
t^2 - 2t - 78 = 0
d= b^2 - 4ac
d= 4 + 312
d= 316
-b±√d/2a
2±2√79/2=1±79.

therefore time taken to hit the ground will be 1+√79
(In the answer 1 is being added, because it is the time taken to reverse the direction of velocity from upwards to downwards. Aa initially the object is moving upwards and then it starts to fall downwards.