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Q.

Two projectiles, A and B are thrown with initial velocities of 60 m/s and 40 m/s at angle $30^{0}$ and $60^{0}$ with the horizontal respectively. The ratio of their respective ranges is $(g = 10 m / s^{2})$

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a

$\sqrt{3} : 2$

b

9 : 4

c

$2 : \sqrt{3}$

d

$4 : 9$

answer is C.

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Detailed Solution

The formula of range of projectile,
$R = \frac{u^{2} \sin 2 θ}{g} R_{1} = \frac{u_{1}^{2} \sin 2 θ_{1}}{g}; R_{2} = \frac{u_{2}^{2} \sin 2 θ_{2}}{g} \frac{R_{1}}{R_{2}} = \frac{u_{1}^{2} \sin 2 θ_{1}}{u_{2}^{2} \sin 2 θ_{2}} \frac{R_{1}}{R_{2}} = \frac{60^{2} \sin (2 \times 30^{0})}{40^{2} \sin (2 \times 60^{0})} = \frac{9}{4}$

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