A ball is thrown vertically up with a velocity `u`. It passes three points `A, B` and `C` in its upward journey with velocities `u/s,u/3` and `u/4`, respectively. Find `(AB)/(BC)`.

Options

A. 1
B. 2
C. `10/7`
D. `20/7`

Answer

D

Explanation

`A rArr v^2 = u^2 - 2gh_1 rArr -2gh_1 = (u/2)^2 - u^2 = (-3u^2)/(4)`
`rArr h_1 = (3u^2)/(2g(4))`
`B rArr (u/3)^2 - u^2 = -2gh_2 rArr h_2 = (8u^2)/(2g(9))`
`C rArr (u/4)^2 - u^2 = -2gh_3 rArr h_3 = (15u^2)/(2g(16))`
`AB = (u^2)/(2g) [ 8/9 - 3/4]`
`BC = (u^2)/(2g) [ 15/16 - 8/9]`
`(AB)/(BC) = 5/36 xx (16xx9)/(7) = 20/7`