How do you solve projectile motion problems?

Projectile motion splits into horizontal (constant velocity) and vertical (accelerated by gravity). Equations: Horizontal: x = v₀cos(θ)·t. Vertical: y = v₀sin(θ)·t - ½gt². Time of flight: t = 2v₀sin(θ)/g. Max height: H = v₀²sin²(θ)/(2g). Range: R = v₀²sin(2θ)/g. Key: horizontal and vertical motions are independent. g = 9.8 m/s². Max range occurs at θ = 45°.