A body is projected from the earth at angle $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \mathrm{~m}$, the maximum height reached by it is : (in metres)

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Aicharya · Accepted Answer

$R=\frac{u^2 \sin 2 	heta}{g}$ $	herefore \quad 20=\frac{u^2 \sin \left(2 	imes 30^{\circ}ight)}{g}$ $\Rightarrow \quad \frac{u^2}{g}=\frac{20}{\sin 60^{\circ}}=\frac{20}{\sqrt{3}} 	imes 2=\frac{40}{\sqrt{3}}$ Now, $H=\frac{u^2 \sin ^2 	heta}{2 g}$ $=\frac{40}{\sqrt{3}} 	imes \frac{\sin ^2 30^{\circ}}{2}$ $=\frac{40}{\sqrt{3}} 	imes \frac{\left(\frac{1}{2}ight)^2}{2}$ $=\frac{5}{\sqrt{3}} \mathrm{~m}$

A body is projected from the earth at angle $30^{\circ}$ with the horizontal with some initial velocity. If…

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