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

(options given in pic)

Answer 1

Hiiii......

Here is answer... (A) ...

As it is thrown upward let with velocity u m/s ....
At max height H .. the final velocity v = 0 ...
Let t be time .....

... u = gt .... (1) by first eqn .. v = u + at ....

As .. S = ut + 1/2 at^2 ...

H = ut - 1/2 g t^2 ..... (2) ....
put ... (1) in (2)...
we get... g = 2H / t^2 ..... (3)....

Now... let v be the velocity at height h ...

v^2 = u^2 - 2gh .... Third eqn ...of motion...

v^2 = (gt)^2 - 2 × 2H/t^2 × h .....from (3) & (1)...

v^2 = 4 / t^2 ( H^2 - Hh ) ...

v = 2 / t ( H^2 - Hh )^0.5 ....

put t = T /2 as T is total time of flight .. upward and then downward...

So ... v = 4/T ( H^2 - Hh )^0.5 .....

Hope u got it.....