JEE Mains · Physics · STD 11 - 3.2 motion in plane
Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\)
- A \(\sqrt{3}: 2\)
- B \(2: \sqrt{3}\)
- C \(1:1\)
- D \(4:9\)
Answer & Solution
Correct Answer
(D) \(4:9\)
Step-by-step Solution
Detailed explanation
\(R_1=\frac{u_1^2 \sin 2 \theta_1}{ g } ; R_2=\frac{ u _2^2 \sin 2 \theta_2}{ g }\) \(\frac{R_1}{R_2}=\frac{u_1^2}{u_2^2} \frac{\sin 2 \theta_1}{\sin 2 \theta_2}=\frac{40^2 \sin \left(2 \times 30^{\circ}\right)}{60^2 \sin \left(2 \times 60^{\circ}\right)}=\frac{4}{9}\)
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