Kinematics

JEE Main level, single correct, medium

239 of 308

Question 239 of 308

Two projectiles are thrown with same initial velocity making an angle of 45∘45^{\circ} and 30∘30^{\circ} with the horizontal respectively. The ratio of their respective ranges will be

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Answer: (C) 2:32:\sqrt{3}

Let projection speed is uu, The formula for the range of the projectile is given by, R=u2sin⁡2θgR=\dfrac{{u}^{2}\sin 2\theta }{g}. Therefore,
R1=u2sin⁡(90∘)g;R2=u2sin⁡(60∘)g{R}_{1}=\dfrac{{u}^{2}\sin \left(90^{\circ}\right)}{g};{R}_{2}=\dfrac{{u}^{2}\sin \left(60^{\circ}\right)}{g}
R1R2=sin⁡90∘sin⁡60∘=23\dfrac{{R}_{1}}{{R}_{2}}=\dfrac{\sin 90^{\circ}}{\sin 60^{\circ}}=\dfrac{2}{\sqrt{3}}

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