I’ve never seen a hawk catch a pigeon, but I once watched a golden eagle make several stoops on a jackrabbit. It was like something out of a Warner Bros. cartoon; the eagle was clumsy and inept and when it came down the rabbit would just jump aside. Eventually the eagle crashed into a sage bush. As it tried to extricate itself from the bush the rabbit merrily hopped around it. Then, seeming more annoyed than scared, the rabbit hopped over to a factory parking lot and hid under a car till the pesky eagle left.
A couple weeks later I was with a birdwatching group and we were looking at whooping cranes and geese at the Bosque del Apache Wildlife Refuge south of Socorro, NM. A coyote approached the cranes and the guide said “You’re about to witness the murder of a ten million dollar bird.” However, all the cranes and geese out in the open watched the coyote carefully, ready to take off if he made the slightest move on them. Knowing this, the coyote ignored them. He made his way to a field of corn stubble where he could crouch down and hide himself from a prospective victim. A few minutes later he came out with an unfortunate goose clamped tightly in his jaws, strolled past the still wary geese and cranes in the open meadow, jumped over a stream as his prey flapped in vain, and ran off into the forest while the birdwatchers shouted “Go Wiley!”