Projectile Range
Gives the horizontal distance a projectile travels before returning to its launch height
The equation
What it solves
Gives the horizontal distance a projectile travels before returning to its launch height. Optimal range occurs at θ = 45°; complementary angles (e.g., 30° and 60°) give equal ranges.
When to use it
Level-ground projectile problems with no air resistance and constant g. The sin(2θ) form is compact but requires the angle to be measured from horizontal.
When NOT to use it
Invalid for uneven terrain (launch ≠ land height). Breaks down with air drag — real maximum-range angles are less than 45°. Do not use on inclined planes without re-deriving the formula.
Common mistakes
Using sin θ instead of sin 2θ — a very common algebra slip. Not recognizing that sin 2θ = sin(180° − 2θ), which means two angles give the same range. Plugging in g = 10 when the problem specifies 9.8 m/s² or 9.81 m/s².