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Physics · MOTION IN A PLANE
हिन्दीTwo projectiles are launched with the same initial speed \( v_o \) at complementary angles of projection \( (45^\circ + \alpha) \) and \( (45^\circ - \alpha) \). The ratio of their horizontal ranges \( R_1 / R_2 \) is:
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Correct answer · Option D
1 : 1
Explanation
For complementary angles \( \theta_1 = 45^\circ+\alpha \) and \( \theta_2 = 45^\circ-\alpha \), \( \sin(2\theta_1) = \sin(90^\circ+2\alpha) = \cos(2\alpha) \) and \( \sin(2\theta_2) = \sin(90^\circ-2\alpha) = \cos(2\alpha) \). Thus \( R_1 = R_2 \), giving ratio 1:1.
