If all thisREALLY matters to you, there is areally good book by Robert Rinker called "Understanding Firearms Ballistics." It is one of the most definitive works on projectile ballistics I have seen. And while it was wriiten about firearms, the principiles are the same as what you are describing here.

The arrow, as it leaves the bow, does NOT travel a straight line. It travels in a parabolic curve, whose rate of fall increases as range increases. This is due to the fact that acceleration due to gravity is not a linear function, but a squared function (acceleration due to gravity = 32 feet per second SQUARED). The arrow starts falling the instant it comes out of the bow, so we must aim the bow upwards (via our sights/line of sight/which IS a straight line) to make this curve that the arrow is traveling intersect with the staight line that our sight follows. The projectile will cross the line of sight twice in any normal setup. It might be possible to set a bow up where you could have the line of sight just barely kiss the tangent of the curve of the parabolic flight of the arrow, but i think it would be too unwieldy to use. And you can launch an arrow perfectly parallel to surface of the earth, it just depends where your target is.