Projectile Range Calculator
Calculate the horizontal range of a projectile launched from ground level using R = v² * sin(2*theta) / g.
Horizontal Range
91.74 m
Horizontal Range vs Launch Velocity
Fórmula
## Projectile Range For a projectile launched from and landing at the same elevation: ### Formula **R = v² * sin(2*theta) / g** Maximum range occurs at a 45-degree launch angle. The range is symmetric about 45 degrees (e.g., 30 and 60 degrees give the same range).
Ejemplo Resuelto
A ball is launched at 30 m/s at 45 degrees.
- 01R = v² * sin(2 * theta) / g
- 02R = 900 * sin(90°) / 9.81
- 03R = 900 * 1 / 9.81
- 04R = 91.74 m
Preguntas Frecuentes
At what angle is the range maximized?
45 degrees gives the maximum range on flat ground, because sin(2 * 45°) = sin(90°) = 1.
Does air resistance affect projectile range?
Yes. This formula assumes no air resistance. In reality, drag reduces both range and maximum height.
Why do complementary angles give the same range?
Because sin(2*theta) = sin(180° - 2*theta). For example, sin(60°) = sin(120°), so 30° and 60° produce equal ranges.
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