Ratio of Horizontal Range for Complementary Angles – Rankers Physics
Topic: Kinematics
Subtopic: Projectile from Height

Ratio of Horizontal Range for Complementary Angles

If a body A of mass M is thrown with velocity \(v\) at an angle \(30^\circ\) to the horizontal and another body B of same mass is thrown with same speed at an angle of \(60^\circ\) to the horizontal, the ratio of range of A and B will be :
\( 1 : \sqrt{3} \)
\( \sqrt{3} : 1\)

1 : 3

1 : 1

Solution:

Horizontal range is given by \(R = \frac{u^2 \sin(2\theta)}{g}\). For complementary projection angles \(\theta\) and \(90^\circ - \theta\) (like \(30^\circ\) and \(60^\circ\)), the horizontal ranges are equal. Thus, the ratio of range is \(1 : 1\).

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