Q62 / 90 · JEE Main 2023 (10 Apr Shift 2) · Physics

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:

A
$\sqrt{3} : 1$
B
$1 : \sqrt{3}$
C
$2 : \sqrt{3}$
Correct answer
D
$1 : 3$

Solution

The maximum height is given by, $H = \frac{u^{2} \sin^{2} θ}{2 g}$ .
The given data is
$θ_{1} = 30 ° θ_{2} = 60 ° u_{1} = u_{2}$
Therefore,
$\frac{{(H_{1})}_{max}}{{(H_{2})}_{max}} = \frac{u_{1}^{2} \sin^{2} θ_{1}}{u_{2}^{2} \sin^{2} θ_{2}} = {(\frac{\sin 30 °}{\sin 60 °})}^{2} = {(\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}})}^{2} = \frac{1}{3}$

Hence, the correct answer is option: 'D'.

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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:

Solution

Relevant Questions

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: