Kostenloser Projectile Range Rechner
Berechnen Sie, wie far a projectile travels horizontally. Kostenloser range Rechner unter Verwendung von launch speed und angle.
Horizontal Range
91.74 m
Horizontal Range vs Launch Velocity
Formel
## 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).
Lösungsbeispiel
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
Häufig Gestellte Fragen
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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