A stone dropped form the top of a tower is found to travel `(5//9)` of the height of tower during last second of its fall. The time of fall is :

Options

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Answer

B

Explanation

The distance from the top `h' = h - (5h)/(9) = (4h)/(9)` is travelled in `(t - 1)` seconds, where t is time of fall on the ground.
`:. (4h)/(9) = (1)/(2) g (t -1)^(2)`
`(4)/(9) ((1)/(2) g t^(2)) = (1)/(2) g (t - 1)^(2)`
`(4)/(9) t^(2) = t^(2) + 1 - 2t`
`5t^(2) - 18 t + 9 = 0`
`(5t - 3) (t - 3) = 0`
`:. t = 3`