JLCM Contest: Jump With Joe

[HeirToPendragon]

It wouldn't matter if you jump to terra firma, you'd have built up so much kinetic energy that you'd kill yourself as soon as you landed.

[Willeth]

So you jump to the other side of the world, and you simply fly straight up into the air. If at any point you are going to go out of orbit you just jump lower. And then when you reach the apex, having lost all momentum, you jump back to the ground.

[HeirToPendragon]

Willeth, Gravity is the same on the other side of the world

[Willeth]

Yes, but direction and momentum isn't. If you are falling directly down on one side, and then jump to the other side, you are then being propelled upwards. The gravity, which pulls to the centre, would then slow your fall, rather than speed it up.

[HeirToPendragon]

No Willeth that wouldn't work. Gravity works like a flat map, not a round globe. If you jump to say China, you're still gonna be falling.

The way you are talking you're thinking that you're going to keep falling as if the world isn't there.

[Willeth]

No. You're wrong. Gravity pulls to the centre of the earth. Momentum is a separate force, which does not depend on the location of the earth, but is affected by gravity. You would still be falling, you'd just be falling in the opposite direction, which is up.

EDIT: Extremely quickly and poorly drawn diagram time!


Red is gravity. Blue is a single path with a jump, green is what was proposed - perpetual falling, followed by my solution for cancelling out the momentum.

[Admiral Amara]

I think Willeth is actually right on this one, assuming momentum is maintained when you reach the other side of your jump. The diagram is truth =o

[Willeth]

Thank you. Apparently H2P still thinks the world is flat. 0_o

[stormothecentury]

Whereas my point is that the laws of physics are pretty much moot for this discussion, so why not take that one extra step and just appear on the earth? Or, for that matter, appear with a horizontal orientation rather than vertical, heading towards some sort of industrial size & strength shock absorber? You know, like Ethan Suplee before he got the surgery or something.

[HeirToPendragon]

Imagine if you just stop the exhaust on a rocket. Sure it had a lot of momentum to get it to go against gravity, but if you turn off that momentum that thing is gonna come crashing back down. The momentum would have to die first sure, but that only takes a few seconds. To do what you're thinking you'd of needed to free fall for hours to work up any sort of momentum to overpower gravity.

I'd do the math, but I am not a physicist. We need to calculate this. Basically we need to figure out have much work is required for a rocket to shoot straight up. Then we'd have to figure out how much force you could build up by free falling (as free fall time approaches infinity). I don't think you'd ever create the necessity to do what you're thinking.

[Admiral Amara]

Actually, since you're building up momentum by falling, you'll only ever reach a certain maximum speed: Terminal Velocity. I'm pretty sure that TV isn't enough to break gravity, so you'd even out pretty quick.

[Silv3r]

H2P I think you've kind of missed the point, although its good to see you concede a bit to momentum.

By teleporting to the opposite side of the earth instead of shooting down toward the earth, you would shoot up into the sky (Force acts in vectors, say if it's midday on the side you telported from, it would be midnight on the opposite side and you would be moving relative to the sun if you want to think in vectors, not relative to the Earth's gravitational pull). Gravity would then use it's force upon your mass, pulling in the opposite direction to your current momentum, eventually reducing your velocity to zero and you having no momentum at which point it would be safe to teleport to terra firma before you start speeding up again.

Its like throwing a ball straight up, at a certain point it stops completely before beginning to descend.

The math would actually be extremely simple, velocities, forces and Earth's gravity are the first things they teach you when dealing with physics.

All this ignores wind resistance etc.
Say the jumper weighs 75kgs (165 lb).
Earth's gravity acts with an accelleration of 9.2m/s^2
Force=Mass*Acceleration
so the force acting upon him is
F= 75 * 9.2 = 690N (Newton's)
No matter where on earth he is.
Momentum = Mass * Velocity
Say he's fallen for 10 seconds
Acceleration = (Vf - Vi)/t
9.2=Vf/10
Vf=92m/s

Look, I could keep going on about this, but essentially, this is alot easier: If he fell for 10 seconds, in order to cancel his momentum he would need the same force acting upon him in the opposite direction for the same amount of time. God why didn't I think of that earlier, I'm not deleting those calculations though, so if you would like to keep working on them for no reason at all, go for your life. If he were to jump starigh to terra firma, a force in the opposite direction would have to be massively greater in order to compensate for the much shorter "falling" time, probably about 0.2 seconds worth, so the force acting directly on his body would be 50 times greater.

[Willethguest]

We need to get xkcd in on this shit.

[MightyLeeMoon]

I'm smarter for having read this thread.

[opie301]

And here's me retracting my initial statement. Turns out that when Davey teleports, all of his momentum is neutralized. Or rather, as Gould explains it in his book, the process of teleportation takes into account the differing frames of reference between point A and point B and compensates for the variables.

A basic physics example that was used in the book is to point out the different velocity one would have in Texas versus New York due to the Law of Conservation of Angular Momentum. Theoretically, if you teleported from Texas to New York, your velocity in the direction of the Earth's rotation should be faster than your surroundings. That you step out with a velocity matching your surroundings should indicate that there some sort of internal compensation within the mechanics of teleportation that correct for these sorts of things.

So essentially, each time you jump, your momentum and velocity is corrected to match for a local, stationary position.

Let's assume, however, that momentum was not canceled after each jump. Silv3r's explanation is correct, so long as the jumper maintains the original frame of reference (i.e. that down, in relation to the sun and other celestial bodies remains the same) after jumping to a point at sea level on the other side of the planet. In that situation you'd be like a pendulum on the upswing. You would have passed your point of highest velocity and would be slowing down, relative to the earth.

But if, as Storm suggests, we're already bending physical laws by allowing instantaneous teleporation between two points, and we accept that our our relative positions in space are adjusted for the local frame of reference, then I suppose we can go one step further and accept that momentum is canceled during transit.