[PSU213]

My extent of physics is a few courses/labs in college, so while I understand the vector discussion, I am by no means an expert.

If the "initial motion" of the ball was toward an opponents endline, I would think its "initial direction" was toward that same endline. At the moment the ball leaves the player's hand(s), it is travelling in a certain direction. If there is no wind (or any other outside force), the ball cannot change the direction of travel.

If the runner is running downfield at 18 mph, parallel to the sideline (and 18 mph is a figure I got from the initial post), and he throws the ball with a velocity of 5 mph parallel to the sideline toward his own goalline, then the ball still has a velocity of 13 mph downfield, relative to the ground (in the X direction, as defined in a previous post). Again assuming no outside forces, that ball has a relative velocity of 13 mph when it leaves his hand and relative velocity of 13 mph when it reaches the hands of a receiver.

Based on this, it would be a foward pass. I believe this came up in the AFC Championship Game a few years ago when NE beat Pittsburgh the first time after a blocked FG by NE. NE returned it for a TD, but there was a question of whether a pass after the ball's recovery was forward or backward. It was ruled backward on the field and replays did not show enough evidence to overturn it.