According to the guys who literally wrote the book about it, well, it depends on the one you ask.
Random guy: Can you jump farther than your movement when you use magic, that is to say jumping jump and stride boots and spring?
Mike Mearls: I would say yes – the intent of the design is to blow you up very far
Jeremy Crawford: To be clear, things like jump spell do not increase speed. You can jump crazy far, but your speed limits it.
On Facebook, "Mike Mearls led the creation of the 5th edition of Dungeons & Dragons, overseeing the development of the game and leading the creation of the D & D scenarios and universes." According to Twitter, Jeremy Crawford is "the chief designer of the #DnD player manual, I answer rule questions here and I compile the answers every month".
Together, they are the co-designers of the game, but Mearls tends to answer for the RAI or its internal rules, while Crawford's answers are supposed to be the official RAWs. I'm not quite sure if random tweets are considered official, or simply the Sage Advice Compendiums.
So, let's look at it from different perspectives.
From a physics point of view, there are three ways to jump further.
1. You can increase your vertical speed (and thus your height) during the jump.
2. You can increase your horizontal speed during the jump.
3. You can decrease your drop rate after the jump.
The jump spell says:
(back leg of a grasshopper) You touch a creature. The creature's jump distance is multiplied by three until the end of the spell.
It is worth mentioning that the material element is the leg of a grasshopper. This strongly implies that the spell strengthens the recipient's strength while jumping. That is, the extra jump distance is most likely caused by 1 or 2 above, not 3.
Ok, so how to increase jump distance with extra speed? Well, that's the basic cinematic, but the essential is:
pthere = ½ To t² + vy0 t
pX = vx0 t
We solve the first equation to know when the vertical position (y) is 0 and we get t = 0 (we started on the ground) and t = ½Avy0. We can substitute this for the second equation to obtain:
d = vx0½ A v y0 = ½ A vx0 vy0
This means that we can triple the jump distance by tripling the vertical or horizontal speed of the jump. If we triple the vertical speed, we also triple the time taken, and the horizontal speed remains unchanged. If we triple the horizontal speed, we jump three times the distance in the same amount of time. We could multiply each by about 1.732 (sqrt of 3) so that it takes 1.732 times longer.
So mathematically, we could go one way or the other. However, there is a strong argument for predominantly horizontal velocity. Jumping higher means that your maximum height is multiplied by 9 = 3² and all this extra power in a vertical jump would allow you to jump even higher. A character of strength 10 could jump (3 + 0) × 9 = 27 feet in the air, while a character of strength 20 could jump (3 + 5) × 9 = 72 feet in the same way. ;air. Or 2.5 × 9 = 22.5 feet tall by jumping 30 feet forward with a force of 10 or 5 × 9 = 45 feet tall by jumping 60 feet forward with a force of 20. Jump faster means your height maximum does not change, and you're just going much further, which seems closer to the design intent here.
So, RAW does not necessarily help much. Clearly, a normal jump is assumed to have about the same speed regardless of the duration of the jump. But it is because it is much easier to use a fixed speed of displacement than to make calculations, and the approximation is not so different from reality. Moreover, who can say that a very big jump does not require extra time to land and reorient, which further mitigates the difference?
One thing that is useful is this:
Long jump. When you take a long jump, you cover several feet up to your strength score. if you move at least 10 feet on foot immediately before the jump.
Clearly, a long jump implies a start in motion. You are not just wasting your time; you make a little dash. This further reinforces the idea that jumping a long distance is a matter of speed and not height.
Using the numbers of the OP:
Normally, you must use 10 moves before the jump, spend up to 10 points for the jump (depending on the strength), then have 5 points to allocate before or after the jump. When the jump spell is used, you only triple the distance you travel, regardless of the jump you make. So for each movement point you skip, you travel a horizontal distance of 3 feet.
RAW vs physics
What really deserves to be emphasized now: if the rules are clearly simplified, more than the equations of physics, they are rather similar to real physics.
Use more physics, based on the numbers above. On Wikipedia, h = gt² / 8. Solving for a height of 8 using 32 ft / s² gives about t = 1.4 s on a force character 20. Jumping 20 feet in 1.4 seconds means that horizontal velocity is about 14 ft / s. The normal walking speed is 30 ft / 6s = 5 ft / s, so it's not crazy. But the character does not jump vertically and horizontally at the same time.
From a forum: at the discretion of your DM, you must pass a DC 10 (athletic) strength test to overcome a low obstacle (no greater than a quarter of the jump distance), like a hedge or a wall.
Thus, during long jumps, your feet are a quarter of the jump distance to the ground, or about 5 feet on a 20-foot jump. This gives us only about 1,118 seconds of airtime. To clear 20 feet in 1,118 sec, the character moves at about 17 feet / sec horizontally or about 3.6 times the normal walking speed.
A very fast sprint is about 45 km / h = 41 ft / s, and our guy reaches about half that distance in 10 feet. In this article, we see the guy with the speed of 41 ft / s, Usain Bolt, accelerates really fast reaching 5.5 m / s (18 ft / s) in about 1 s, about 15 feet.
Similarly, the longest jump recorded was nearly 30 feet, the longest typical jumps being around 25 feet, without being congested. So a jump of 20 feet is not crazy. Note that true jumpers generally have a greater acceleration distance, giving them a take-off speed of between 12 and 35 ft / s, with normal 20 ° jump angles somewhere in the middle, but our 20-speed guy accelerates quickly instead of going smoothly. (Also note that the 20 ° angle still corresponds to the idea that we are primarily looking for the speed of advancement and not the vertical height.)
In addition, this is the type of physics that the game is supposed to simulate as precisely as possible in simplified rule systems. So, "it's an imaginary world" is not a good counter-argument in this case.
So using physics as a guide is a good start.
Ok, the physics plus a bit of RAW as well as the description of the spell indicate that jumping with the jump spell should mean that you are traveling about three times faster. Other people say that you travel at the same speed. How does it work in practice?
If we assume that you travel faster by jumping further under effects like this, everything seems to work. You can try to cheat by walking 29 feet then jumping 60, but that does not work. You can only use your force in movement points to jump at each turn, and you can not use as many movement points as you have; you have just traveled three times further for each point used. So if you walk 29 feet then jump, you go up 3 feet, for a total of 32. If you walk 20 feet then jump, you go up to 30 feet, for a total of 50 feet.
However, if we say that your jump distance is limited by your speed, we have a problem. Say you walk and see a ravine. It's 60 feet wide. Your companion wizard launches Jump on you, so you have a whole minute to cross. You climb the ravine, then in the last 10 feet, you jump and jump 60 feet, easily cleaning the ravine. Woot!
Then you turn around and realize that a goblin assassin is about to ambush your sorcerer friend! You shout at him so that he is not surprised, then go through to help him. Except you can not. You can not quite understand, but because of something metagame called "we are in combat now", you can not exceed 30 feet in one turn, and 10 of them are the dash departure. So you can only go half way before falling into it.
Ok, of course, you can use the dash ability to go even further in a trick. But out of combat, you did not have to do it. And the jump spell is clearly an automatic dash action in order to jump. So you should not duty. In addition, the dash gives you only 60 feet, and the first 10 are used to start the jump, leaving you 10 feet short. So, you have to take a complete turn run action, when you should be able to jump through the ravine with your basic move, use a dash to add 30 feet of movement and approach the goblin, then hit it in the face with your standard action.
Physics, real-world athletes, extrapolation from basic movement rules and description of the spell, tell us that your movement speed should increase when you jump using the Jump spell. The ability of your character to run and jump changes inexplicably between non-combat and in combat, which is really strange. And one of the developers of the game says that you should be able to jump very far, because that is the design intent.
So, in your example, you can move 10 feet, use 10 of your remaining movement points to quickly jump 30 feet, then move an additional 5 feet before or after the jump, using your movement.
But, to put all this in the skin, a different game developer (in this case, the one whose word is probably the official interpretation on RAW) says nothing of the above is true, and you are stuck at a normal traveling speed without any sense here. And the fact that there is no explicit RAW explaining how to handle a partial displacement distance means that some DMs will be reluctant to call it an official rule.
But I see it as an obvious interpretation of RAW.