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 in nth second
`S_n = u + a/2 (2n-1)`
`rArr (9h)/(25) = g/2 (2n - 1)`
Distance travelled in n sec
`h = 1/2 gn^2`
`rArr 9/25 . 1/2 gn^2 = g/2 (2n-1)`
`9n^2 - 50n + 25 = 0`
`n = (50pm sqrt(2500-900))/(18) = (50 pm 40)/(18)`
`= 90/18 and 10/18 = 5 and 5/9`
`n = 5sec`
`h = 1/2 xx 9.8 xx (5)^2 = 122.5m`