Projectile Motion: The Physics of Throwing Things
Published Apr 13, 2026 · 6 min read
Any object launched into the air follows a parabolic path. Horizontal motion is constant; vertical motion is affected by gravity (9.8 m/s²).
Key Equations
| Quantity | Formula |
|---|---|
| Range | R = v²sin(2θ) / g |
| Max height | H = v²sin²(θ) / 2g |
| Time of flight | T = 2v·sin(θ) / g |
The 45° Rule
Maximum range occurs at a 45° launch angle (ignoring air resistance). In practice, air resistance means the optimal angle is slightly less — about 40-43° for most sports.
Real-World Examples
- Basketball free throw — Optimal angle is about 50-55° due to the height of the basket
- Soccer goal kick — Maximum distance at ~40° considering air drag
- Water fountain — The parabolic arc is projectile motion in action
Try it: Use our Projectile Motion Calculator to compute range, height, and flight time for any launch.