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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Range of a projectile ： ウィキペディア英語版 Range of a projectile In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range. The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight. The maximum horizontal distance traveled by the projectile * g: the gravitational acceleration—usually taken to be 9.81 m/s2 (32 f/s2) near the Earth's surface * θ: the angle at which the projectile is launched * v: the velocity at which the projectile is launched * y0: the initial height of the projectile * d: the total horizontal distance travelled by the projectile. When neglecting air resistance, the range of a projectile will be : $d\; =\; \backslash frac\; \backslash left(\; v\; \backslash sin\; \backslash theta\; +\; \backslash sqrt\; \backslash right)$ If (y0) is taken to be zero, meaning the object is being launched on flat ground, the range of the projectile will then simplify to : $d\; =\; \backslash frac\; \backslash sin(2\backslash theta)$ == Ideal projectile motion == Ideal projectile motion states that there is no air resistance and no change in gravitational acceleration. This assumption simplifies the mathematics greatly, and is a close approximation of actual projectile motion in cases where the distances travelled are small. Ideal projectile motion is also a good introduction to the topic before adding the complications of air resistance. === Derivations === 45 degrees goes the farthest. This is due to the nature of right triangles. Additionally, from the equation for the range : : $R\; =\; \backslash frac$ We can see that the range will be maximum when the value of $\backslash sin\; 2\; \backslash theta$ is the highest (i.e, when it is equal to 1). Clearly, $2\; \backslash theta$ has to be 90 degrees. That is to say, $\backslash theta$ is 45 degrees. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Range of a projectile」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.