Error what is the v_s variable in this code:
Argh, sorry. That one is supposed to be "v_p" - as in "velocity of (soccer) player". Why is it "v_s"? Probably because in the process of thinking about this, I actually thought in german, a language that uses the word "spieler" for "player". Sorry.

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Gumby22:
The diagrams would definately be helpful, but I do have a few questions

delta is supposed to be the angle, right? Then shouldn't you use vec_dot and either normalize this vector vec_sub(guyPos,ballPos) or divide by its length? (ballDir has the length 1 according to your definition, so thats fine).
To get the angle then, we'd have to do "acos", but since we're only going to use "cos" anyway, we can simply keep it like that, but then, we shouldn't have "cos(delta)" and instead "just" delta.
I suppose you also need to put smoe brackets between the "timefactor"-line.
The next line, however, is where I have most problems - guyDir is, as I understand it, a vector, right? But in the "guyDir"-line, you use both constant numbers (270, to be exact), as well as vector"pointers" (vec_sub). Maybe you want guyDir to be an angle, but then, you'd have to make the resulting "vec_sub-vector" into a "number".
ARGH. Okay, I... am confused.

I don't know about the other users, but I would certainly have an easier time if you could provide diagrams or your scribble page
