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Physics · MOTION IN A PLANE
हिन्दीTwo projectiles are thrown with the same initial speed \( v_0 \) from ground level at complementary angles of projection \( \theta_1 = 45^\circ + \alpha \) and \( \theta_2 = 45^\circ - \alpha \) (where \( 0 < \alpha < 45^\circ \)). If \( h_1 \) and \( h_2 \) are the maximum heights attained by them respectively, what is the ratio \( \frac{h_1}{h_2} \)?
Correct answer · Option 2
\( \tan^2(45^\circ + \alpha) \)
Explanation
\( h_1 = \frac{v_0^2 \sin^2(45^\circ + \alpha)}{2g} \) and \( h_2 = \frac{v_0^2 \sin^2(45^\circ - \alpha)}{2g} = \frac{v_0^2 \cos^2(45^\circ + \alpha)}{2g} \). Therefore, \( \frac{h_1}{h_2} = \frac{\sin^2(45^\circ + \alpha)}{\cos^2(45^\circ + \alpha)} = \tan^2(45^\circ + \alpha) \).
