Depends on how outside the box you want to go. If you have HERO system or Champions available, I'd look at the "move through".
I'd let him use the jump as part of his move an make an acrobatics check, with a DC of 10 plus fall damage. If he suceeds, he can attack as normal, adding a +2 to damage as per charge.
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I'd let him use the jump as part of his move an make an acrobatics check, with a DC of 10 plus fall damage. If he suceeds, he can attack as normal, adding a +2 to damage as per charge.
I believe this, or something very similar to it, is how we've resolved the situation as well. You basically have a charge and a fall to resolve. I don't think there's much in the core rules to arbitrate this situation, so a good houserule like the ones mentioned is probably the best resolution.
The second.
The logic is he successfully timed his land to absorb the shock of landing still able to make the attack.
This roll won't get rid of the falling damage. Course, if it's less than 10 feet, it'll almost always auto succeed unless they little or no ranks in acrobatics.
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No real need to go outside the box.
PC jumps from a height. Normal jumping rules apply, acrobatics checks to mitigate damage, etc. PC should be technically jumping to an open square next to the enemy, same as a charge takes you to a square next to them (see notes at end for houserules regarding jumping directly on enemy).
PC gets a bonus similar to charging (+2 hit/-2 AC). Assuming PC hits enemy, enemy takes the normal damage of the hit and extra damage equal to being a "dense, heavy material" of a size equal to the PC, to account for the weapon's purpose as a lethal instrument and the mass of the falling PC. An average medium PC will add 3d6 damage by doing this.
Is this worth doing off of jumps higher than 20', due to damage and the fact you end up prone if you take any lethal damage from a fall? Not really. But that seems to me to be in line with real-world expectations. A leaping barbarian doing 1d12+10+3d6 is going to destroy just about anything he his, in the "real world" levels of 1-4.
I use ride checks opposed by acrobatics (jumping bonuses apply, its the bucking bronco concept) checks for the purposes of actually staying on top of a creature, usually with a CMB check (grapple) to start, although I would allow a "freebie" check after a jump down attack like this, assuming the attack itself was successful. Failed attack, or failed check, land next to it likely prone. Successful, stay on the creature Shadow of the Colossus style, and enjoy denying it the pleasure of it's dexterity bonus against your attacks.
I wouldn't add 3d6. After all, its not the character crashing into the target but only his weapon. I think that makes jumping too good. I don't want to get into the silly situation where a fighter jumps off his horse to gain extra damage from height.
I think +2 to hit from charging and +1 for high ground is sufficient. Maybe give a small damage bonus, not more than 1d6.
How would a monk's slow fall ability factor in?
Like normal. If they fell 50 ft before the attack, and have 50ft worth of slow fall, then the DC is 10.
We also add that as the attacker leaves the threatened area they are subject to an AOO (just like jumping). No additonal damage is added as it is normal weapon damage. Then resolve the landing as normal under falling, slow falling, acrobatics etc.