If you can suspend your disbelief that a high-level Barbarian with a normal greatsword, in the core rules, can cut a 2-inch-thick iron or steel door in half with one stroke, then you should be able to accept a guy throwing someone 60 feet through raw physical prowess and extreme training. Not to mention shrugging off/mostly-evading a dragon's acid-breath that's strong enough to liquify that same door, and keep on fighting at full strength. And jump over a 56-foot chasm without difficulty.
Half-orc barbarian 20 with greatsword, full Power Attack, Mounted Combat, Ride-By Attack, Spirited Charge, 24 Strength (base 18, +2 racial, +4 from levels), and Mighty Rage (+8 Str) can do 2x(2d6+56) damage in 3.5E. A standard iron or steel door has hardness 10 and 60 hp. (thinking about it, there's no core way to break down that door with one stroke without using Spirited Charge; I come up 1 damage short if going half-orc brb16/fighter4 with greater rage and weapon specialization; without Spirited Charge they need a non-core feat, like Powerful Lunge or Melee Weapon Mastery; at least to do the trick completely nonmagically and without a non-core prestige class)
Aforementioned Barbarian can get a Jump bonus of +23 from ranks, +7 from Str, +4 from Mighty Rage, +4 from fast movement, +4 from the Run feat, +2 from the Athletic feat, and +2 synergy from 5 Tumble ranks (not hard to get by that point, only an exceedingly stupid barbarian wouldn't have the 10 skill points to spare over the course of their career). A total bonus of +46, for an average running Jump result of 56.
