Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is [2023]

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Solution

Q.
Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is [2023]

1 2 : $\sqrt{3}$

2 $\sqrt{3}$ : 1

3 1 : 3

4 1 : $\sqrt{3}$

Ans.
(3)

$H_{\max} = \frac{u^{2} \sin^{2} θ}{2 g}$

$\frac{H_{1}}{H_{2}} = \frac{\sin^{2} θ_{1}}{\sin^{2} θ_{2}} = \frac{1}{3}$

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