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(D) The horizontal range $R$ of a projectile is given by the formula: $R = \frac{v_{0}^{2} \sin(2	heta)}{g}$,where $v_{0}$ is the initial velocity,$\

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$R_{A}=R_{C} < R_{B}$

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(D) The horizontal range $R$ of a projectile is given by the formula: $R = \frac{v_{0}^{2} \sin(2	heta)}{g}$,where $v_{0}$ is the initial velocity,$	heta$ is the angle of projection,and $g$ is the acceleration due to gravity.Since $v_{0}$ and $g$ are constant for all three projectiles,$R \propto \sin(2	heta)$.For projectile $A$: $	heta_{A} = 30^{\circ}$,so $R_{A} \propto \sin(2 	imes 30^{\circ}) = \sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.For projectile $B$: $	heta_{B} = 45^{\circ}$,so $R_{B} \propto \sin(2 	imes 45^{\circ}) = \sin(90^{\circ}) = 1$.For projectile $C$: $	heta_{C} = 60^{\circ}$,so $R_{C} \propto \sin(2 	imes 60^{\circ}) = \sin(120^{\circ}) = \sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.Comparing the values: $R_{A} = \frac{\sqrt{3}}{2}$,$R_{B} = 1$,and $R_{C} = \frac{\sqrt{3}}{2}$.Therefore,$R_{A} = R_{C} < R_{B}$.

Three projectiles $A, B$ and $C$ are projected at an angle of $30^{\circ}, 45^{\circ}, 60^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are the ranges of $A, B$ and $C$ respectively,then (velocity of projection is the same for $A, B$ and $C$):

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