The Jet Dash Feat says that it doubles the distance you can jump; does this mean that a horizontal jump DC is equal to half the distance traveled, or that the restriction on not being able to jump further than your remaining speed is modified?
Specifically, a level 5 character with Athletics as a class skill, 5 ranks invested in Athletics, a STR of 14, and a speed of 30' can move 10', and jump a maximum of 20' (remaining speed) at a DC of 20 by taking 10 (10 + 5 + 3 + 2).
How does this character's ability to jump differ with Jet Dash?
The feat just says double the distance you can jump.
I'd say if given the rules and situation without the Jet Dash feat the character could jump up to 20', then with the Jet Dash feat, they can jump 40'.
Without a FAQ or errata otherwise, that seems the simplest way to go.
That of course would let you use Jet Dash and jumping to go faster than your normal land speed, although it requires a check to do so. This isn't the only place in the rules where you can make a skill check to improve your speed. Having a climb speed lets you also make a skill check to increase your speed to double.
The feat lets you double your jump distance.
With a running start, if you roll a 15 on Athletics check to long jump, instead of 15 feet, you jump 30 ft.
With a running start, if you roll a 20 on Athletics check to high jump, instead of 5 feet, you jump 10 ft.
It doesn't change the limits on Athletics check where you use the remainder of your movement.
Specifically, a level 5 character with Athletics as a class skill, 5 ranks invested in Athletics, a STR of 14, and a speed of 30' can move 10', and jump a maximum of 20' (remaining speed) at a DC of 20 by taking 10 (10 + 5 + 3 + 2).
How does this character's ability to jump differ with Jet Dash?
The difference for a character with Jet Dash would be that they only needed an Athletics check of 10 to jump 20 feet. Or DC 20 for 20 feet with no running start.
The feat is more limited when only considering long jump with regular default speed.
However it's much more useful with high jumps as the modified DC is only 2x height wanted instead of original 4.
It's also useful if you don't have a chance for running start. The long jump and high jump DCs would be equal to no-Jet Dash Athletics running start DCs.
If wanting to benefit from greater long jump distance get speed suspension augmentation to increase speed, or other methods to increase speed. Or you run (with Jet Dash that'll be 6 x speed) and you'll have all the movement needed for even Jet Dash modified jump distances.
The feat lets you double your jump distance.
With a running start, if you roll a 15 on Athletics check to long jump, instead of 15 feet, you jump 30 ft.
With a running start, if you roll a 20 on Athletics check to high jump, instead of 5 feet, you jump 10 ft.It doesn't change the limits on Athletics check where you use the remainder of your movement.
To play Devil's advocate, if they wanted to change just the DCs of the jump check, why didn't they just say that? They simply said double the distance you can jump. There's a rule saying you can jump X feet for every X you roll with a running start (modified by situation). There is also a rule saying you can jump a distance no greater than your remaining amount of movement. Why does Jet Dash treat these two rules differently?
How far can my character without the Jet Dash feat and a 30 foot move speed, horizontally jump with a 10 foot running start and an athletics check result of 40?
Why is the answer to that question not doubled when I add the Jet Dash feat to it?
If wanting to benefit from greater long jump distance get speed suspension augmentation to increase speed, or other methods to increase speed. Or you run (with Jet Dash that'll be 6 x speed) and you'll have all the movement needed for even Jet Dash modified jump distances.
I don't think the rules allow you to run and jump. Run is a full round action where you move 4 times your speed (or 6 six times your land speed with Jet Dash). Jump under athletics explicitly states:
"As part of a move action, you can use Athletics to horizontally
or vertically jump a distance no greater than your remaining
amount of movement."
It could be argued you can't jump farther than a single move action's worth of movement, and can only do so with an explicit move action to move. Of course, if you are suggesting that wording does allow you to jump while running, then the following wording from climb speed,
"You can move your full climb speed when you use the move
action while climbing, but you cannot run. You can move double
your climb speed with a successful Athletics check to climb, but
you take a –5 penalty to the check.",
implies you can double your climb speed while running with climb (if you have Gravity boost, which overrides the no running clause).
I'll note Jet Dash under the more permissive interpretation would still never let you move more than double your speed, similar to the climb double move restrictions. Given that Climbing master can let you move twice your land speed in a single move action with a trivial, allowed to take 10 on climbing check, I'd say allowing Jet Dash to let you jump up to twice your speed with a much harder check isn't game breaking.
Also, I'd like to take this opportunity to state the jump rules are a bit non-intuitive. A character with a 30' move speed can physically jump a 25 foot chasm from a standing start, but can't from a 10 foot running start.
Oh that's a good point about the running and jumping stating needing a move action.
The part of the jump limit is from a Pathfinder precedent:
You are always considered to have a running start when jumping, you add your kineticist level as a bonus on all Acrobatics checks to jump, you jump twice as far or high as the results of your check indicate, and you can accept 1 point of burn when jumping to double the distance you jump again (to a total of four times as far).
Mark Seifter basically explains (unofficially in his Ask Anything thread but he wrote the wild talent and it's the only precedent I can find for this situation) that benefit would benefit high jumps.
The feat allowing one to double the jump distance and jump rules stating the jump uses up the remainedsr of movement wouldn't be Jet Dash treating the rules differently, just that it would only benefit specific instances of jumping (not rolling maximum jump distance in distance or height).
The only reason that rule exists for acrobatics is so they didn't have to have rules for what happens when you are in the air after the end of your turn.
Even with speed suspension, it's trivial with the feat to hit the "cannot jump further than remaining movement" limitation. At level 12 (complete speed suspension) a PC can run 10' and take 10 to jump 50' with a DC 25 just by strength and the speed bonus (+12) to reach the limit of movement. Add any ranks in athletics and you exceed your movement range.
At 20th level, with 20 ranks, +3 from class skill, +12 from 60' move speed via suspension (30+30), and +5 from strength, a character can jump 25' from a standstill by taking 10. With a running jump, they can jump 50' of their DC 50 check.
The same character with Jet Dash could make the standing jump a 50' jump... and can jump either 50' with a 10' running start.. or 100'. Depending on what the feat means when it says "double".
Yes. As established, making long jumps is pretty easy even without the feat.
The feat greatly helps high jumps though.