Supposed you try launching a party member across a 500 feet wide and 50 feet deep gap with a trebuchet. however, something goes horribly wrong and he's launched straight down into the pit (let's just say he was stuck in the bag until it reached the end). this would launch him at about 3X the speed of a normal fall (150 feet per second instead of 55 feet per second). Does he still take only 5d10 falling damage (1d10 per 10 feet), or does he take more like 15d10 damage because he lands at triple speed?
You are absolutely and entirely outside rules territory from the moment you've decided to fire someone out of a trebuchet and into the ground, so only loose inferences from the rules are going to help us here. But let's see what it gives us to work with.
Forewarning: if you're after real-world simulation in D&D 4e, you've come to the wrong town. The designers consciously eschewed real-world simulation in order to just make a fun and well-balanced game, so 4e runs on simplistic game logic that laughs in the face of our Earthen physics. 4e has squircles for instance: consider that the circle is defined as a shape where every side is equidistant from the center, and that this perfectly describes a square room of any size as far as a walking PC is concerned. Instead of attempting to draw real-world physics out of D&D 4e—which 4e will either directly contradict or simply not help you with—use the game logic, leave the calculator aside and use your time to beat stuff up and do fun things instead.
this would launch him at about 3X the speed of a normal fall (150 feet per second instead of 55 feet per second).
You have some parts of this conclusion wrong.
First, there's nothing that makes him fall faster. You have a trebuchet, but we don't know how fast he's actually traveling: D&D 4e doesn't exactly have specific rules for trebuchets that I'm aware of, unless you'd like to point us to them.
Second, the speed of a normal fall is 500 feet per round, at the end of the creature's turn (Rules Compendium, p209, High-Altitude Falls). Since a round is 6 seconds, that's actually 83.33 (recurring) feet per second, and nobody ever falls faster than this. That's far less than the falling speed of a skydiver (who is trying to fall slowly), so we can assume accurate simulations of Earth physics and wind resistance are to be left well aside: things work differently here.
So. Your orc hits the ground normally, and takes the normal amount of fall damage.
If they hit the wall instead, we don't know if they're really traveling fast enough to even simulate it with an equation that works from 500 feet/second of fall damage. You're in house rule territory, and we've established D&D 4e doesn't really care about what physics has to say about falling, so make a judgement call with a small portion of fall damage, or decide your character survives it fine because they might as well.
Alternately, whilst I would not advise against firing D&D 4e characters out of trebuchets on account of how awesome that is, I would at least just advise saying they succeed and skipping this trouble.
Unless they're an enemy NPC, in which case I advise they die hilariously.
No, it's not. There are no physics here, there is only zuul.
We can model a "flung from trebuchet" as a fighter-flinger doing level-appropriate damage.
Assuming that your party member wants to be there, we can take the hit lines:
Hit: The target flies 2d6 squares in a random direction. It takes 2d8 + 5 damage, and lands prone at the end of its movement.
And just adjust the 2d8+5 to be level+5 (with appropriate dice swinginess)).1
We then just calculate fall damage from the ground down, using the appropriate hazard or trap. If the pit isn't a hazard or trap, fall damage tells us that:
Falling Damage: A creature takes 1d10 damage for each 10 feet it falls, to a maximum of 50d10.
Or level+5d10+5 damage from the total attack and drop.
It seems like you're trying to adjudicate failure on a skill challenge, would you like help with that? ::clippy popup sound::
Looking at "The idea is that there's a MALS (Magically Assisted Landing Site) at the other end that makes the landing survivable." suggests that this is a fairly cool way of getting over a wall or equivalent (otherwise the suggestion is "just walk around the gap, it hurts less"). In this instance, failures in the skill challenge should not represent falling short and dropping to your doom. Instead, they should be priced as a loss of healing surges due to the wall impact or other things going wrong. Especially as failure in this skill challenge isn't interesting (since it, in the main, either resolves to character death or "try again"), abstracting the damage to "lose a few surges as you impact the wall and climb up" works far more effectively than "you fall, you are [healed | dead], you try again."
By having the skill challenge be "how closely do you clip the wall as you fly over, and what else goes wrong?" failure maps to a more informed enemy, less healing surges during the upcoming fights, and potentially harder enemies to represent the failure of reinforcements or materiel to arrive. It doesn't map to "go roll a new character."
1 Yes, this means trebuchets do more damage as the PCs level up. They're just that much more cool astral jet-assisted trebuchets in epic level. Embrace the awesome. Play a different system for physics.
If you want to be quite realistic, assume the character falls from higher altitude. How much would the character elevates if he was fired upward? That's the adjust you must make in altitude.
According to Loren Pechtel, the distance the character would go up is 1/4 of the range that it was intending to fire him.
e.g.: Let's say the range of firing someone on the trebuchet is 100 ft. That means that person fired vertically would go 25 ft up. The fall is of 50 ft. When fired down, you apply a fall of 75 ft.
That's the way you can apply a little more realism, without bothering with a lot of calculations.