Okay Jeff, most of your last post was spot on. We are saying pretty much the same thing, just in different ways.

The reason the arrow does not travel a straight line is because as soon as it leaves the bow, gravity begins to accelerate the arrow towards the earth at 32 fps squared. The farther the arrow falls, the faster it falls... Acceleration due to gravity is not a linear function (it will not plot as a straight line on a graph), it is a squared function, which means it's rate of fall gets faster the further it falls. It will plot as a curve on a graph. If it fell at a steady rate all of your sight pins would be the same distance apart, but we know this is not true. The further the distance the further apart the pins get. This is due to two factors, one, the force of gravity keeps accelerating the arrow towards earth faster and faster, and it is compounded by the fact that the arrow is slowing down horizontally because of airresistance, allowinggravity more time to work on the arrow.

You see, this is really a problem ruled by time... Once there is nothing left holding the arrow up in the air,resticting it's fall, the effects of gravity take over.

In theory, in a vaccuum, disregarding the curvature of the earth, you could shoot an arrow perfectly parallel to the earths surface at the exact same instant that you dropped a second arrow, and they would both hit the ground at the same time. This fact really takes folks aback the first time they hear it, but it is true. Both arrows are accelerated towards the earth at the same speed due to gravity, it is acting on both arrows equally. One just travels a much farther horizontal distance before it impacts the earth.

The law? I think it had to do with that Newton guy and the apple. Sorry, don't know the number of that law, but I'm sure it's in the top five laws of physics.

As far as your picture dipictions, I saw nothing wrong on them that needed to be corrected. Sorry if you took my post that way.