Projectile Max Height

This formula gives the highest point a projectile reaches when it is launched and then moves under gravity alone, assuming air resistance is negligible. It comes from splitting the launch velocity into vertical and horizontal parts: only the vertical component, v sinθ, determines how high the object rises, and gravity slows that upward motion until the vertical speed becomes zero at the top. Using the constant-acceleration equation for vertical motion leads to H = (v^2 sin^2θ) / (2g).

Use this when analyzing the peak height of a kicked ball, thrown object, launched projectile, or any motion where the object follows ideal projectile motion. It is especially useful in sports science, physics problems, and trajectory calculations where launch speed and angle are known.

• Using cosθ instead of sinθ, which gives the horizontal component instead of the vertical one
• Forgetting to square the sine term or the speed, which changes the result a lot
• Using a different value of g without checking units, especially mixing m/s² with other gravity values