Calculating Point-blank Range
A projectile falls due to gravity once it leaves a weapon barrel. All objects at the same geographic location fall with the same acceleration, denoted g, roughly 9.8 m/s² (32 ft/s²). Velocity is a vector; the vertical component of any projectile's velocity can be treated separately from the horizontal component. If the barrel is horizontal and at height h above the ground, then Newton's equations of motion can be used to show that the range is approximately, where v is the muzzle velocity. This calculated range is reduced by air resistance. The air resistance depends on at least the frontal area of the projectile, the drag coefficient, air density and obviously the speed of the projectile—making the problem a differential equation.
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