A body is projected upwards with a velocity `u`. It passes through a certain point above the ground after `t_(1)`, Find the time after which the body passes through the same point during the journey.

Options

A. 1`((u)/(g)-t_(1)^(2))`
B. `2((u)/(g)-t_(1))`
C. `3(u^(2)/(g)-t_(1))`
D. `3(u^(2)/(g)-t_(1))`

Answer

B

Explanation

Suppose `v` be the velocity attained by the body after time `t_(1)`,
Then `v=u-gh_(1)` (i)
Let the body reach the same point at time `t_(2)`. Now velocity will be downwards with same magnitud `v`. Then
`-v =u -g t_(2)` (ii)
(i) -(ii) `rArr 2v=g (t_(2)-t_(1))`
or `t_(2)-t_(1) =(2v)/(g) =(2)/(g) (u-g t _(1))=2 ((u)/(g-t_(1))`.