# Projectile motion analysis ### Key concepts * Maximum height ($h$) reached by a projectile launched at angle $\theta_i$ with initial speed $v_i$ is given by: - $$h = \frac{v_i^2 \sin^2 \theta_i}{2g}$$ [9](#page=9) * Range ($R$) of a projectile launched over a flat surface at angle $\theta_i$ with initial speed $v_i$ is given by: - $$R = \frac{v_i^2 \sin(2\theta_i)}{g}$$ [9](#page=9) * Maximum range occurs when $\theta_i = 45^\circ$, with $R_{max} = \frac{v_i^2}{g}$ [9](#page=9).