Note how gingerly this coyote initially pursues his prey in this video. He begins by listening for little scurrying sounds of voles in their vast tunnel network underground -- he does not want to alert them to his presence. So he tiptoes around the spot, carefully positions himself and waits -- all the while listening intently. He's very smart about what he is doing: clever and shrewd.
Here's a wonderful little post from Coyote Yipps on the hunting habits of the coyote. It illustrates nicely the manner in which they jam their snouts into the earth (at, for example, 2:21) whilst attempting to root out rodents. (I never cease to be impressed by the strong schnozes of canines. I once met a dog, a wonderful border collie named Syd, who played basketball voraciously, using her nose to steal the ball from any human antagonist. I was always worried, but after seeing film of foxes, wolves, and now coyotes thrusting their faces into the earth, I can see that Syd knew that her lovely face was in no danger.)