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Q.

A stone projected at an angle of 60^o from the ground level strikes at an angle of 30^o on the roof of a building of height 'h' . Then the speed of projection of the stone is:

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a

$\sqrt{g h}$

b

$\sqrt{6 g h}$

c

$\sqrt{2 g h}$

d

$\sqrt{3 g h}$

answer is C.

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Detailed Solution

Let initial and final speeds of stone be u and v.

$\begin{array}{l} ∴ v^{2} = u^{2} - 2 g h . . . . . (i) \\ and v \cos 30^{\circ} = u \cos 60^{\circ} . . . . . . (ii) \end{array}$

solving 1 and 2 we get

$u = \sqrt{3 g h}$

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A stone projected at an angle of 60o from the ground level strikes at an angle of 30o on the roof of a building of height 'h' . Then the speed of projection of the stone is: