Wile E. Coyote and Axioms

I keep having a recurring nightmare where I am trapped in the following axiom system:

A1: Coyotes and roadrunners live on the surface of a perfectly round planet.
A2: Coyotes always begin chasing roadrunners exactly 2 seconds after the roadrunner passes them.
A3: Coyotes can only catch roadrunners if they can catch up to them after having chased them.
A4: Roadrunners run faster than coyotes.
A5: Coyotes stop chasing roadrunners when they disappear from view.
A6: All coyotes have 20/20 vision.

Will I be able to catch the roadrunner in this axiom system? If not, add other axioms to the system, which are consistent with A1 through A6, that will ensure that I will always catch the roadrunner. Justify your claims! I'll need a professional report. Help me - you're my only hope!

Hungry as ever,
Wile E. Coyote

Be sure to satisfy the writing assignment criterion and the proof checklist.

Take a look at the sample report solution for a different writing assignment (in a different class) in order to get an idea of how to satisfy the writing assignment criterion.

When working on the first question, you might look at a proof by examining the following two cases:
If the coyote can see the roadrunner...
Otherwise the coyote can't see the roadrunner and so he has no hope of catching him.

When working on the second question, you must justify why the axiom(s) that you've added are consistent with A1 through A6 and then justify why the coyote will always be able to catch the roadrunner in this new axiom system.