A particle is dropped under gravity from rest from a height h(g=9.8) and it travels a distance 9h/25 in the last second,the height h is
Let us assume that the particle takes time t to reach the ground.
D ( in last sec ) = 9h/25
The particle covers (h - 9h/25) = 16h/25 in (t - 1) sec.
Using equations of motion
16h/25 = (1/2)g( t - 1)2 ... (A)
Also, h = (1/2)g( t )2 ... (B)
Solving equation (A) and (B),
=> (16/25)t2 = (t - 1)2
=> 4t = + (5t - 5)
or, t = 5 sec.
t = 5/9 is rejected because in question it is given that t>1 as the body covers 9h/25 in last sec
So, h = (1/2)g (5)2 = (25)(9.8) / 2 = 122.5