A body is projected upwards with 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 return journey.

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Solution

Suppose v be the velocity attained by the body after time $t_{1}$ .Then v = u - g $t_{1}$ ...(i)
Let the body reaches the same point at time $t_{2}$ . Now velocity will be downward with same magnitude v, then
-v = u - $g t_{2}$ ...(ii)
(i) - (ii) $\Rightarrow$ 2v = $g (t_{2} - t_{1})$
or $t_{2} - t_{1} = \frac{2 v}{g} = \frac{2}{g} (u - g t_{1}) = 2 (\frac{u}{g} - t_{1})$

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A body is projected upwards with velocity u.It passes through a certain point above the ground after t1. Find the time after which the body passes through the same point during the return journey.

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A body is projected upwards with 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 return journey.