A body projected vertically upwards with a given velocity. The ratio of the times taken to cover the first one fourth and the last one fourth of the ascent to the highest point is.

Options

A. `1 : (2 - sqrt(3))`
B. `2 : (2 - sqrt(3))`
C. `(2 - sqrt(3)) : 1`
D. `(2 - sqrt(3)) : 2`

Answer

C

Explanation

`t_2 = sqrt((2(h//4))/(g))`
`t_2 = sqrt((h)/(2 g))`
`t_1 = sqrt((2 h)/(g)) -sqrt((2(3h))/(g))`
=`sqrt((h)/(2g)) [2 - sqrt(3)]`
`t_1 : t_2 = (2 - sqrt(3)) : 1`.