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 only 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? If needed, can you 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! Help me - you're my only hope!

Hungry as ever,
Wile E. Coyote