Question

Three particle $A,B$ and $C$ are projected from the same point with same initial speed making angles ${30}^{\circ },{45}^{\circ },{60}^{\circ }$respectively with the horizontal. Which of the following statements is correct

• A. $A,B$ and $C$ have unequal ranges
• B. Ranges of $A$ and $C$ are equal and less than that of $B$.
• C. Ranges of $A$ and $C$ are equal and greater than that of $B$.
• D. $A,B$ and $C$ have equal ranges

Answer 1

Answer: (B)

Ranges of $A$ and $C$ are equal and less than that of $B$.

$R_{{30}^{\circ }}=\frac{u^2\sin {60}^{\circ }}{g}=\frac{\sqrt{3}}{2}\left(u^2/g\right)$

$R_{{45}^{\circ }}=\frac{u^2\sin {90}^{\circ }}{g}=\frac{u^2}{g}$
$R_{{60}^{\circ }}=\frac{u^2\sin {120}^{\circ }}{g}=\frac{u^2\cos {30}^{\circ }}{g}=\frac{u^2}{g}\left(\frac{\sqrt{3}}{2}\right)$
$R_{{30}^{\circ }}=R_{{60}^{\circ }}<R_{{45}^{\circ }}or{R}_A=R_C<R_B$