A stone falls freely from rest from aheight `h` and it travels a distance `9h//25` in the last second. The value of `h` is

Options

A. 145m
B. 100m
C. 122.5m
D. 200m

Answer

C

Explanation

Distance travelled by the stone in the last second is `(9h)/(25) = (g)/(2) (2t-1) ( :. u=0)`
Distance travelled by the stone in t s is
`h= (1)/(2) g t^(2)` (using `s= ut + (1)/(2) a t^(2)`) `(9)/(25) = ((2t-1))/(t^(2)) rArr 9t^(2) -50t + 25 =0`
Solving, we get `t= 5s or t= (5)/(9) s`
Substituting t= 5s in (ii), we get
`h= (1)/(2) xx 9.8 xx (5)^(2) = 122.5m`