Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is [2023]

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Solution

Q.
Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is $(g = 10 {m/s}^{2})$ [2023]

1 1 : 1

2 4 : 9

3 2 : $\sqrt{3}$

4 $\sqrt{3}$ : 2

Ans.
(2)

$R_{1} = \frac{u_{1}^{2} \sin 2 θ_{1}}{g}, R_{2} = \frac{u_{2}^{2} \sin 2 θ_{2}}{g}$

$\frac{R_{1}}{R_{2}} = \frac{u_{1}^{2} \sin 2 θ_{1}}{u_{2}^{2} \sin 2 θ_{2}} = \frac{40^{2} \sin (2 \times 30 °)}{60^{2} \sin (2 \times 60 °)} = \frac{4}{9}$

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