A stone falls freely from rest from aheight `h` and it travels a distance `h//2` in the last second. The time of journey is

Options

A. `sqrt(2) s`
B. `(2-sqrt(2)) s`
C. `(2+sqrt(2)) s`
D. `2 s`

Answer

C

Explanation

Let t: time of journey.
h: displacement in t second
`h/2`: displacement in last second
`h=1/2g t^(2) …(i)`
`h/2=1/2g(2t-1) …(ii)`
`(1)/(2).1/2g t^(2)=1/2g(2t-1)`
`t^(2)-4t+2=0`
`t=2+sqrt(2)=3.41 s`
`t=2-sqrt(2)=0.59 s`
`t=(2-sqrt(2))` second is not possible, because time of journey is greater than 1 s.