We have a very fast dog, about 50lbs, thin and long legged, about 4 years old, and a squirrel in the yard one day who already knows our dog well was caught out in the open, and the dog ran at it, and off they went, and just when he was going to get it, it took an amazing 90 turn like in just an instant, sharper than I imagined possible, and the dog went right past and then as the dog realized and turned to look the squirrel ran past him and off they went but now the squirrel was close enough to a tall evergreen tree and made it.
So, they seem to have a very good sense of speed and angle and timing!