Why do you step on a cockroach, swat at a fly, etc.? On the farm I use to always carry a gun in the tractor. When running the tractor theywould pass right by you. First time you put it in park, or even let off the throttle....they would take off very quickly. Don't feel sorry for the coyote, they are smart buggers and will do just fine for themselves. There is one in Central Park (New York City), is that the one you are referring to Krunch?
By the way, yes it could have gotten your cat, but I would doubt it. Rabitts are a much easier meal. We had about 12 ducks at one time. One morning there were 10 left, next morning 6, next morning 3, next morning 1. You should have seen the look on that last ducks face. Next morning no ducks.