The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are R 1, R 2 and H 1, H 2 respectively. Choose the correct option:

(A) {R}_{1}>{R}_{2} and {H}_{1}={H}_{2}

(C) {R}_{1}<{R}_{2} and {H}_{1}<{H}_{2}

(D) {R}_{1}={R}_{2} and {H}_{1}={H}_{2}

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JEE Mains · Physics · STD 11 - Motion in plane

JEE Mains 2021
Medium
MCQ

The ranges and heights for two projectiles projected with the same initial velocity at angles \(42^{\circ}\) and \(48^{\circ}\) with the horizontal are \({R}_{1}, {R}_{2}\) and \({H}_{1}\), \({H}_{2}\) respectively. Choose the correct option:

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \({R}_{1}={R}_{2}\) and \({H}_{1}<{H}_{2}\)

Step-by-step Solution

Detailed explanation

Range \({R}=\frac{{u}^{2} \sin 2 \theta}{{g}}\) and same for \(\theta\) and \(90-\theta\)

So same for \(42^{\circ}\) and \(48^{\circ}\)

Maximum height \({H}=\frac{{u}^{2} \sin ^{2} \theta}{2 {g}}\)

\({H}\) is high for higher \(\theta\)

So \({H}\) for \(48^{\circ}\) is higher than \({H}\) for \(42^{\circ}\)

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