Angle of Projection for Equal Height and Range – Rankers Physics

Ground to Ground Projectile: Practice Problem & Solution

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 Explained:

To solve this problem, we apply the core principles of Ground to Ground Projectile. Understanding the underlying formula is key to arriving at the correct answer below:

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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