A balloon rises from ground when a stone is dropped from balloon at a given instant it takes a time 2u/g, ( u is constant) to reach ground irrespective of position from where it is dropped. Find acceleration of balloon as a function of time
Asked by hariom2083
16th July 2018,
12:46 PM
Answered by Expert
Answer:
Let h be the height when the stone is dropped from ballon. Let v be the ballon velocity when the stone is dropped.
Then for the stone, we can write, S(t) = h + v×t - (1/2)×g×t2 ..................(1)
where S(t) is vertical distance travelled by the stone as a function of time.
It is given that at t = (2u)/g , stone reaches ground, i.e., S(t) = 0 when t = (2u)/g.
hence from eqn.(1) we write, 
we write the eqn. for balloon speed as, 
In above eqn.(3), the expression for v(τ) is written using eqn.(2)
Differential eqn. (3) is solved as follows.
now we write expression for h(τ) using eqn.(4), 
from eqn.(5) and eqn.(3), we can write
Answered by Expert
18th July 2018,
3:42 PM
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