Question

Three projectiles $A$, $B$ and $C$ are projected at an angle of ${30}^o$, ${45}^o$, ${60}^o$ 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

The correct option is D $R_A=R_C<R_B$

Range of projectile motion, $R=\frac{u^{2}sin\left(2\theta \right)}{2g}$

$⟹$ $R\propto sin\left(2\theta \right)$ $(\because u$ is same for all $)$

Given : ${\theta }_A={30}^o$ ${\theta }_B={45}^o$ ${\theta }_C={60}^o$

We know: $sin\left({60}^o\right)=0.866$ $sin\left({90}^o\right)=1$ $sin\left({120}^o\right)=0.866$

$⟹$ $R_A=R_C<R_B$