Why Balls Make Parabolas

Toss a ball. It rises, slows, peaks, and falls. The path traces an exact parabola. Why? Horizontal position grows linearly with time (no forces act sideways), while vertical position changes quadratically (gravity pulls constantly). Combining gives y = ax² — the classic parabolic equation.

Galileo confirmed this in 1638 by rolling balls down inclined planes. Before him, philosophers guessed projectile paths were straight lines. Galileo proved otherwise with measurements, establishing the quadratic law of falling bodies — the first precise equation describing real motion.