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

A) A,B and C have unequal ranges
B) Range of A and C are less than that of B
C) Range of A and C are equal and greater than that of B
D) A,B and C have equal ranges
Explanation

(b) When a body is projected at an angle $\theta$ with the horizontal with initial velocity $u$, then the horizontal range $R$ of projectile is
$R = \frac{u^{2}\sin{2\theta}}{g}$
Clearly, for maximum horizontal range $\sin{2\theta = 1\ \ or\ 2\theta = 90{^\circ}\ or\ \theta = 45{^\circ}.\ }$ Hence, in order to achieve maximum range, the body should be projected at $45{^\circ}$.
In this case
$R_{\max} = \frac{u^{2}}{g}$
Hence, range of $A$ and $C$ are less than that of $B$.

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.