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  4. A stone is dropped from a height h, simultaneously another stone is thrown up from the ground which reaches at a height 4 h, the two stones cross each other after time :-

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Q. A stone is dropped from a height $h$, simultaneously another stone is thrown up from the ground which reaches at a height $4 h$, the two stones cross each other after time :-

Motion in a Straight Line

Solution:

image
If $u$ is the velocity of projection,
then $0=u^{2}-2 g(4 h)$
$\therefore u =\sqrt{8 gh }$
Now $y=\frac{1}{2} g t^{2}$ ...(i)
and $h - y = ut -\frac{1}{2} gt ^{2}$ ... (ii)
From above equations, we have
$t =\frac{ h }{ u }=\frac{ h }{\sqrt{8 gh }}=\sqrt{\frac{ h }{8 g }}$