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Q.

A body is projected upwards at an angle 30° to the horizontal and the range is R₁. Another body is projected upwards at an angle 60° with the horizontal and the range is R₂. If both the bodies have the same initial speed, then

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a

$2 R_{2} = R_{1}$

b

$R_{2} = 2 R_{1}$

c

$R_{1} < R_{2}$

d

$R_{1} = R_{2}$

answer is D.

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Detailed Solution

$\begin{array}{l} R = \frac{u^{2} \sin 2 θ}{g} and R_{1} = u^{2} \frac{\sin (30^{0} \times 2)}{g} = \frac{u^{2} (\sqrt{3} / 2)}{g} \\ R = \frac{u^{2} \sin (60^{0} \times 2)}{g} = \frac{u^{2} \sin (120^{0})}{g} = \frac{u^{2} (\sqrt{3} / 2)}{g} \\ ∴ R_{1} = R_{2} \end{array}$

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