How far can a Small Cat jump if it uses Sprint?

[ShroudedInLight]

Sprint (Ex)

Spoiler:

Once per hour, a small cat can move at 10 times its normal speed (500 feet) when it makes a charge.

Jump DC Modifiers

Spoiler:

Faster Base Movement: Creatures with a base land speed above 30 feet receive a +4 racial bonus on Acrobatics checks made to jump for every 10 feet of their speed above 30 feet. Creatures with a base land speed below 30 feet receive a –4 racial bonus on Acrobatics checks made to jump for every 10 feet of their speed below 30 feet. No jump can allow you to exceed your maximum movement for the round.

Running Jump: For a running jump, the result of your Acrobatics check indicates the distance traveled in the jump (and if the check fails, the distance at which you actually land and fall prone). Halve this result for a standing long jump to determine where you land. Also, see Pole.

So, normally a Charge allows for double movement and an attack. However, in this case the Charge allows for 500ft of movement. Half of that is 250, which would give the Small cat a jump bonus of something insane like +88 to Acrobatics which would allow it to jump 88+1d20+Skill bonus.

Now that is absolutely insane, however, the Cat can move 500ft in the round and still attack at the end of it while charging...which is also rather insane when you think about it, since this is all taking place over 6 seconds which is 83.3ft per second.

Naturally that increase in momentum would correlate into an increase in Jump Distance, but the cat Jumping 88 feet is a little too high. At the same time, the cat's normal move speed of 50 only would give it a measly +8 circumstance bonus.

How would you rule this?

[Eltacolibre]

Lions can jump surprisingly high...this seems actually pretty accurate when compared to real life.

But anyway if you are worried about it for some reason, there isn't many reason for the small cat to jump like that.

[Kobold Catgirl]

So, you're saying if I get myself a small cat animal companion, I basically have a once per day flying mount?

[ShroudedInLight]

Once per hour actually, 88ft at least horizontal jump in a straight line.

Upwards is 1ft per 4 DC, so it's 22ft straight up or some combination of the two. Take 4ft off the horizontal jump per foot you go vertically.

You would need to be small or medium and take Undersized mount, but it does come online at level 4.

I'm not so much worried about it as I am excited, because if this works I can have my Small Cat jump across from ship to ship and maul casters to death thanks to the Silence I like to cast on it.

[Aureate]

Kobold Cleaver wrote:

So, you're saying if I get myself a small cat animal companion, I basically have a once per day flying mount?

Sprint is once per hour. With kobold wings, could you direct the cat to jump, dismount mid air and glide from there?

Kobold Gliding Wings:

Some kobolds are born with wings that, while too weak for actual flying, do allow them to fall at a very slow and safe pace. A kobold with wings can use them to glide. It can make a DC 15 Fly check to fall safely from any height without taking falling damage, as if using feather fall. When falling safely, it may make an additional DC 15 Fly check to glide, moving 5 feet laterally for every 20 feet it falls. This racial trait replaces crafty.

EDIT: NVM, you don't get that much vertical height.

[Howie23]

Sprint does not increase base move. Jump modifier is based on base speed. RAW is the measly +8. If that doesn't work for your style of play, houserule it to work for you.