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(D) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$,where $u$ is the initial speed and $	heta$ is

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$R_1 = R_3 < R_2$

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(D) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$,where $u$ is the initial speed and $	heta$ is the angle of projection.Since $u$ is constant for all three balls,$R \propto \sin(2	heta)$.For $	heta_1 = 15^{\circ}$,$R_1 \propto \sin(30^{\circ}) = 0.5$.For $	heta_2 = 45^{\circ}$,$R_2 \propto \sin(90^{\circ}) = 1$.For $	heta_3 = 75^{\circ}$,$R_3 \propto \sin(150^{\circ}) = \sin(180^{\circ} - 30^{\circ}) = \sin(30^{\circ}) = 0.5$.Thus,$R_1 = R_3 = 0.5 	imes \frac{u^2}{g}$ and $R_2 = 1 	imes \frac{u^2}{g}$.Comparing these,we get $R_1 = R_3 < R_2$.

Three balls of same masses are projected with equal speeds at angles $15^{\circ}, 45^{\circ}$,and $75^{\circ}$. If their ranges are $R_1, R_2$,and $R_3$ respectively,then:

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