Two bodies \(P\) and \(Q\) are projected on the same horizontal plane, with the same initial speed but at different angles of \(30^{\circ}\) and \(60^{\circ}\) respectively to the horizontal. Neglecting air resistance, what is the ratio of range of \(P\) to that of \(Q\) ?
A. \(1: 1\) B. \(1: \sqrt{3}\) C. \(\sqrt{3}: 1\) D. \(1: 2\)
Correct Answer: A
Explanation
\begin{array}{ll} \text { Range }=\frac{u^{2} \sin 2 \theta}{g} \\ \text { Body P } & \text { Body Q } \\ \frac{u^{2} \sin 2 \theta}{g} & \frac{u^{2} \sin 2 \theta}{g} \\ \theta=30^{\circ}, & \theta=60^{\circ} \\ \frac{u^{2} \sin 60}{g} & \frac{u^{2} \sin 120}{g} \end{array} Ratio of range \(\frac{u^{2} \sin 60}{g} \div \frac{u^{2} \sin 120}{g}\left(\begin{array}{c}u \text { and } g \\ \text { are the } \\ \text { same for } \\ \text { both bodies }\end{array}\right)\) \(\frac{\sin 60}{\sin 120}=1: 1\)
