Angle of Projection for Equal Height and Range – Rankers Physics
Topic: Kinematics
Subtopic: Ground to Ground Projectile

Angle of Projection for Equal Height and Range

At what angle to the horizontal should an object be projected so that the maximum height reached is equal to the horizontal range?
\( tan \theta = 2 \)
\( tan \theta = 4 \)
\( tan \theta = \frac{2}{3} \)
\( \theta = 3 \)

Solution:

Maximum height \(H = \frac{u^2\sin^2\theta}{2g}\) and range \(R = \frac{2u^2\sin\theta\cos\theta}{g}\). Equating the two yields \(\frac{\sin^2\theta}{2} = 2\sin\theta\cos\theta\), which simplifies to \(\tan\theta = 4\).

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