Jack Russell Terriers are an amazing breed. I have one that is extremely gentle and who loves all people and is friendly to all other dogs.
However, should a vermin like a field rat, squirrel or rabbit venture into her domain; her terrier instinct locks in and she is a dedicated killer.
As far as a long legged sight hound's movement goes, see this greyhound video clip.
https://www.youtube.com/watch?v=3wtuZzeulmI
I placed the cursor on he dog's back and noticed that there was very little bobbing up and down...