Projectile Motion - Maximum Height

\[H = \frac{v_0^2 \sin^2(\theta)}{2g}\]

H = maximum height (m)

v0 = initial velocity (m/s)

theta = launch angle (rad)

g = gravitational acceleration (m/s²)

This equation calculates the maximum vertical height reached by a projectile during ideal projectile motion.

Use this formula when analyzing projectile trajectories without air resistance and when the initial velocity and launch angle are known.

If a projectile is launched at 30 m/s with an angle of 60°:

H = (30² × sin(60°)²) / (2 × 9.81) = 34.4 m

Ballistics, sports science, engineering simulations, trajectory prediction, and physics education.

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