If body travels half of its path in the last second of its fall from rest, find the time and height of its fall.

Explanation

Suppose t is the time of free fall
`S_(n)=(g)/(2)(2n-1) and S=(g)/(2)(n^(2))`
`(S_(n))/(S)=((2n-1)xx(g)/(2))/(n^(2)xx((g)/(2)))=(1)/(2)`
`n^(2)-4n+2=0` and `n=(2+sqrt(2))sec`