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

Using the relation , `v^(2) -u^(2) = 2aS`, we have
For motion from O to A , `u^2/4 - u^(2) = 2 (-g)h_(1)`
For motion from O to B For , `u^2/9 -u^(2) = 2 (-g) h_(2)`
For motion from O to C, `u^(2) =2 (-g) h_3`
`:. AB = h_(2) - h_(1) =u^(2) /(2g) [8/ -3/4] =u^2/(2g) xx5/36 `
`BC = h_(3) -h_(2) =(u^2)/(2g) [(15)/(16) -8/9] =u^2/(2g) xx 7/44`
`:. (AB)/(BC) = 5 / 36 xx (144)/7 = 20/7`