Anyone who is shoved off a ledge should travel horizontally as normal and then drop straight down. So, if you are 5 feet from the edge and pushed 8 feet, you travel 5 feet to the edge, 3 feet further, and then straight down.
This sentence made me think of the classic physics problem of determining a cannon ball's trajectory given an initial impulse and gravity. It's a well worn problem whose solution is an equation that has been deeply studied and is easy to compute. This is probably the very equation the game uses for projectiles and shoved characters. The problem is that it doesn't really work for shoving on flat terrain because, for the enemy to travel any distance, the initial impulse needs to be angled upward, if only slightly.
I'd wager most of the distance travelled when getting shoved on flat terrain is the body rotating from vertical to horizontal. Professional athletes playing in contact sports don't lift their opponents, which is difficult and inefficient, but try to use their weight against them. All this to say that hacking the cannon ball equation to function for flat terrain shoving has obvious side effects when shoving from a ledge.
I'm not sure it's possible to reconcile both needs (flat shoving and ledge shoving) with one equation. You could add an air friction term to limit horizontal speed and make ledge shoves more realistic, but that might break the small arc used for flat shoving. You could angle the initial impulse much higher and make it stronger to make the impact spots more realistic though the trajectories would be hilarious. My guess is for both situations to feel right, the game needs to treat them seperately.
In any case I'd like to see an overhaul to the entire projectile arc system because arrows don't arc like that, nor do magic missiles and certainly not bodies.
