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Range of a projectile
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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 = \frac \left( v \sin \theta + \sqrt \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 = \frac \sin(2\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 = \frac
We can see that the range will be maximum when the value of \sin 2 \theta is the highest (i.e, when it is equal to 1).
Clearly, 2 \theta has to be 90 degrees. That is to say, \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)
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