免费抛体射程计算器
计算斜抛运动的水平射程。
m/s
degrees
m/s²
Horizontal Range
91.74 m
Horizontal Range vs Launch Velocity
公式
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).
计算示例
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
常见问题
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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