The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\cir

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The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1:x$. The value of $x$ is

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Sol. [Key Concept: Range $\propto sin2	heta$, so the ratio of ranges $= \frac{\sin 30^{\circ}}{\sin 60^{\circ}}$.]$${R_{1} = \frac{u^{2}sin2 	imes 15^{\circ}}{g} }{R_{2} = \frac{u^{2}sin2 	imes 30^{\circ}}{g} }{\frac{R_{1}}{R_{2}} = \frac{sin30^{\circ}}{sin60^{\circ}} = \frac{1}{\sqrt{3}} = \frac{1}{x} }{x = \sqrt{3} }$$

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