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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 $‘h= 30\,m ’$ . Find the speed of projection(in $m/s$ ) of the stone
$30$
$40$
$50$
$60$
Solution
$\mathrm{V}_{\mathrm{y}}^{2}=\mathrm{u}_{\mathrm{y}}^{2}+2\left(\mathrm{a}_{\mathrm{y}}\right) \mathrm{y}$
$\frac{\mathrm{V}_{\mathrm{y}}}{\mathrm{u} \cos 60}=\tan 30$
$ \Rightarrow \mathrm{V}_{\mathrm{y}}=\mathrm{u} \times \frac{1}{2} \times \frac{1}{\sqrt{3}}=\frac{\mathrm{u}}{2 \sqrt{3}}$
$\mathrm{u}_{\mathrm{y}}=\mathrm{u} \times \frac{\sqrt{3}}{2}$
$\frac{\mathrm{u}^{2}}{12}=\frac{3 \mathrm{u}^{2}}{4}-2 \mathrm{g} \times 30$
$\frac{2}{3} \mathrm{u}^{2}=600 $
$\Rightarrow \mathrm{u}^{2}=900$
$ \Rightarrow \mathrm{u}=30 \mathrm{m} / \mathrm{g}$
