Three particles A,B and C are projected from the same point with same initial speeds making angles $30^{0}, 45^{0} and 60^{0}$ respectively with the horizontal. Which of the following statements is correct

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A,B and C have unequal ranges

Ranges of A and C are equal and greater than that of B

A, B and C have equal ranges

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

answer is B.

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Detailed Solution

$R_{30^{0}} = \frac{u^{2} \sin 60^{0}}{g} = \frac{\sqrt{3}}{2} (u^{2} / g)$ $R_{45^{0}} = \frac{u^{2} gin 90}{g} = u^{2} / g$ $R_{60^{0}} = \frac{u^{2} \sin 120^{0}}{g} = \frac{u^{2} \cos 30^{0}}{g} = \frac{u^{2}}{g} (\sqrt{3} / 2)$
So, $R_{30^{0}} = R_{60^{0}} < R_{45^{0}} or R_{A} = R_{C} < R_{B}$