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 same point at time `t_(2)`. Now velocity will be downwards with same magnitude `v`, then
`-v = u - g t_(2)`....(ii)
Eqn. (i) - (ii)
`2v = g (t_(2) - t_(1))`
or `t_(2) - t_(1) = (2v)/(g) = (2)/(g) (u - g t_(1)) = 2 ((u)/(g) - t_(1))`