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

Answer

B

Explanation

Suppose v be the velocity attained by body after time `t_(1)` then `v=u-g t_(1)` …(i)
Let the body reach the samepoint at time `t_(2)` now velocity will be downwards with same magnitude v, then `-v=u-g t_(2)` …(ii)
`(i)-(iii)implies2v=gU(t_(2)-t_(1))`
or `t_(2)-t_(1)=(2v)/(g)=(2)/(g)(u-g t_(1))=2((u)/(g)-t_(1))`