Question

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 ranges of $A, B$ and $C$ respectively, then (velocity of projection is same for $A, B$ and $C$)

• A. $R_A = R_B = R_C$
• B. $R_A = R_C > R_B$
• C. $R_A < R_B < R_C $
• D. $R_A = R_C < R_B$

Answer 1

Answer: (D)

Range of projectile motion, $R=\frac{u^{2} \sin (2 \theta)}{2 g}$
$\Longrightarrow \quad R \propto \sin (2 \theta) \quad(\because u$ is same for all $)$
Given : $\theta_{ A }=30^{\circ} \quad \theta_{ B }=45^{\circ} \quad \theta_{ C }=60^{\circ}$
We know: $\sin \left(60^{\circ}\right)=0.866 \quad \sin \left(90^{\circ}\right)=1 \quad \sin \left(120^{\circ}\right)=0.866$
$\Longrightarrow \quad R _{ A }= R _{ C }< R _{ B }$