Question

a small body is thrown vertically up which reaches a maximum height H and whose total time of flight is T. Its velocity at a height h will be

Answer 1

Initial vertical speed = u.
Maximum Height H is reached at time T/2. So v=0 at T/2.

0 - u = - g T/2
u = g T/2.

Velocity v at height h is:
v^2 = u^2 - 2 *g * h
= g^2 T^2 /4 - 2 g h
find v by square root

Answer 2

Hey there !!!!!

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Body is thrown vertically up So when body reaches its maximum height ''H''  final velocity (v)=0 ( velocity at maximum height)

Now,

v=u+at

at maximum height 

0=u-gt

u=gt

Time taken for body to reach maximum height (time of ascent) = t

Time taken to reach ground (time of descent)=time of ascent=t

Total time of flight (T) = time of ascent +time of descent = 2t

                 T=2t

                t=T/2

v²-u²=2gh

v²-(gt)²= -2gh

v²= -2gh+g²t²

v²=g²T²/4-2gh

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Hope this helped you..........