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Originally Posted by Dan_ref
A parabola is motion along a "2 dimensional" plane (a plane is 2D by definition so there's no other type) and it describes the vertical flight of an object as a function of time with zero drag (no atmosphere) and does factors in the force of gravity.
I'm not sure what to make of the rest of your post.
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Good points, Dan. I wasn't as precise as I could have been. I should have compared an object traveling in a straight line to one tracing the path of a parabola in a plane. My point was that the forward velocity is not effected by the force of gravity.
Two bullets shot at the same muzzle velocity, but with one subjected to gravity and one not, would both reach a point along the x-axis at the same time. The only difference is that the one not subjected to gravity would be at a higher point along the y-axis. This is despite the fact that the gravitationally affected bullet would have traveled a greater distance due to its more curved path. The important concept to grasp is that the motion made in two directions by this bullet takes place simultaneously, so that it doesn't take any more time to cover the greater distance.
Thus I and the laws of physics disagree with Dexter's premise that the ball which traveled a greater distance would have had to move at a higher average speed in order to reach the destination at the same time.