First slide

Vertical projection from ground

Question

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time $\sqrt{\frac{x h}{y g}}$ . Find x+y.

Easy

A

8
B

9
C

4
D

7

Solution

For first stone $u = 0$ and
For second stone $\frac{u^{2}}{2 g} = 4 h \Rightarrow u^{2} = 8 g h$
$∴ u = \sqrt{8 g h}$

Total distance to be covered is ‘h’ where the initial velocity of stones are
where, t = time to cross each other.
$∵ h_{1} + h_{2} = h$
$\frac{1}{2} g t^{2} + \sqrt{8 g h} t - \frac{1}{2} g t^{2} = h \Rightarrow t = \frac{h}{\sqrt{8 g h}} = \sqrt{\frac{h}{8 g}}$

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