## is projectile motion 3 dimensional or 2 dimensional?

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muheedmir007
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### is projectile motion 3 dimensional or 2 dimensional?

Soupspoon
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### Re: is projectile motion 3 dimensional or 2 dimensional?

What is your current understanding? Under what constraints is your projectile operating, and which freedoms? What are your frames of reference? Is this homework?

Flumble
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Projectile motion is 0-dimensional, as proven by Zeno.

doogly
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Do you know what a dimension is? Can you throw something and check what happens?
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gmalivuk
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### Re: is projectile motion 3 dimensional or 2 dimensional?

It's at least 4-dimensional, and possibly 10 or 26 depending on your preference of string theory.

Though admittedly the motion in one or more of those dimensions is generally considered negligible.
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doogly
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### Re: is projectile motion 3 dimensional or 2 dimensional?

I had to do coriolis acceleration in Physics 1, and look how well I turned out! Grumble grumble.
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LaserGuy
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### Re: is projectile motion 3 dimensional or 2 dimensional?

muheedmir007 wrote:can any one answer this please

Go outside and throw a rock. How many spatial dimensions does it take to describe the path? Now repeat the experiment using a frisbee. Does that change your answer?

Soupspoon
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### Re: is projectile motion 3 dimensional or 2 dimensional?

LaserGuy wrote:
muheedmir007 wrote:can any one answer this please

Go outside and throw a rock. How many spatial dimensions does it take to describe the path? Now repeat the experiment using a frisbee. Does that change your answer?

Warning: If you live in a glass house, do not attempt the first experiment.
Warning: If you live in a Nerf house, you can attempt the second experiment but watch out for light breezes. Like you already have to, unless you've not yet found the right neighbours and like moving every time there's a light gust.

Qaanol
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Pretty sure it’s one-dimensional, though depending on your universe that 1D path may be embedded in some other topology.
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DewOnTheGrass
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Simple projectile motion (interpreted as throwing a ball straight forward w/o any outside forces except gravity and initial thrust) would be three-dimensional: The ball travels away from you (1), up, then down (2), and through time (3), thus travelling through three dimensions. If there is wind (not parallel to the ball's trajectory), then the ball also travels laterally, bringing our total to four.

Eebster the Great
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Qaanol wrote:Pretty sure it’s one-dimensional, though depending on your universe that 1D path may be embedded in some other topology.

Only if the projectile is pointlike.

Kodomo
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Assuming that you have a "point like" projectile (size negligible relative to it's mass) shoy "upwards" in a gravity well (or 45° to maximize reach).

In a flat universe perspective (Newton): It describes a parabolic trayectory that needs two coordinates to describes properly. One is the upward direction (opposite to the "gravity") and one horizontal (that on ideal circunstances) keep velocity constant. There is more ways to decompose the coordenate frames, but this is the most intituive.

Curved (relativity). Here there is no gravity "force", just a "deformed" space. And due the projectile doesn't get any perturbatios (ej: friction) it keeps constant energy in it's reference frame. You could say it's movement is only in 1D, but that dimention is bent alongside the curved space-time.

But real life should consider fricction and viscosity, so you have neither of thoose. Because wind can bend your trajectory sideways, and the drag steals energy of the system and that get you off your linear trajectory in the curved space-time.

morriswalters
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### Re: is projectile motion 3 dimensional or 2 dimensional?

muheedmir007 wrote:can any one answer this please
Well sure, anyone can. If you don't understand coordinate systems it would be a terrible waste though. If you do understand them then why are you asking? Read about coordinate systems and frames of reference. Then come back and ask a better question.

doogly
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Pretty sure they're not coming back, so now it's just a contest to see who can say the cleverest thing about dimensionality.
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Eebster the Great
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### Re: is projectile motion 3 dimensional or 2 dimensional?

According to this, there are no twice differentiable planar fractal curves, so I guess we can say with some confidence that projectile motion must have an integer dimension, as no force field could ever produce motion along a fractal dimensional path.

doogly
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### Re: is projectile motion 3 dimensional or 2 dimensional?

That's begging the question though.
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Eebster the Great
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### Re: is projectile motion 3 dimensional or 2 dimensional?

How's that? Projectile motion by definition is the motion of an object subject to forces, and force is directly proportional to the second derivative of position. If a path is not twice differentiable, then it cannot be produced by any such force, even a discontinuous force. So such a path is impossible for projectiles.

ConMan
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Eebster the Great wrote:How's that? Projectile motion by definition is the motion of an object subject to forces, and force is directly proportional to the second derivative of position. If a path is not twice differentiable, then it cannot be produced by any such force, even a discontinuous force. So such a path is impossible for projectiles.

Except if you go up to general relativity, where projectile motion is just "motion along a geodesic", so you don't need to worry about forces, but you do need to worry about whether you can define a manifold in a fractal space that conforms to the appropriate tensor equations (and I don't even know if you can have a fractional dimensional tensor, so that's about as far as I can get in the problem).
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### Re: is projectile motion 3 dimensional or 2 dimensional?

doogly wrote:Pretty sure they're not coming back, so now it's just a contest to see who can say the cleverest thing about dimensionality.
Your face is a plane in 2 dimensions.?.¿
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Weeks wrote:
doogly wrote:Pretty sure they're not coming back, so now it's just a contest to see who can say the cleverest thing about dimensionality.
Your face is a plane in 2 dimensions.?.¿

Your momma's soooo fat... that any trajectory past her involves a horizontal planar component that is predominantly a hyperbolic orbital segment!

Eebster the Great
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### Re: is projectile motion 3 dimensional or 2 dimensional?

ConMan wrote:
Eebster the Great wrote:How's that? Projectile motion by definition is the motion of an object subject to forces, and force is directly proportional to the second derivative of position. If a path is not twice differentiable, then it cannot be produced by any such force, even a discontinuous force. So such a path is impossible for projectiles.

Except if you go up to general relativity, where projectile motion is just "motion along a geodesic", so you don't need to worry about forces, but you do need to worry about whether you can define a manifold in a fractal space that conforms to the appropriate tensor equations (and I don't even know if you can have a fractional dimensional tensor, so that's about as far as I can get in the problem).

That paper is admittedly specific to plane curves, which I had considered, but I would be pretty surprised if twice differentiable fractal (or more specifically, self-affine) curves could exist on any manifold. Perhaps it is an open (in this case, not yet considered) question. The abstract does point out that smooth self-affine curves do exist, in spite of common sense to the contrary.

doogly
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Eebster the Great wrote:How's that? Projectile motion by definition is the motion of an object subject to forces, and force is directly proportional to the second derivative of position. If a path is not twice differentiable, then it cannot be produced by any such force, even a discontinuous force. So such a path is impossible for projectiles.

Yeah, I feel like "No fractal paths" and "Paths well modeled as solutions to F=ma" are equivalent. If someone is imagining something moving along a fractal path, they are probably imagining some deviation form vanilla Newton 2.

Or maybe they are imagining a dumb thing, like just making F super wonky but still keeping F=ma nice and bedrocky. That is not going to get them a fractal and I suppose it is a content-ful result to tell them they are wrong. So yes, this is good. I un-complain.
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cyanyoshi
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### Re: is projectile motion 3 dimensional or 2 dimensional?

In 2D space, 3D space, and all-higher-dimensional space, Brownian motion has Hausdorff dimension 2. If you model a projectile as being bombarded with a continuum of air particles, then I believe projectile motion is just a transformation away from a Wiener process. We should therefore be able to conclude that projectile motion traces out a fractal with dimension 2, if my intuition is right.

Derek
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### Re: is projectile motion 3 dimensional or 2 dimensional?

Eebster the Great wrote:The abstract does point out that smooth self-affine curves do exist, in spite of common sense to the contrary.

I would like an example of such a curve. Preferably with a picture. The above paper cites a Russian paper for this claim.

Tomaso
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### Re: is projectile motion 3 dimensional or 2 dimensional?

muheedmir007 wrote:can any one answer this please

That depends on the situation:
The rock has no momentum. -> It stands still. Dimension = 0
The rock has momentum. -> It flies in a straight line. Dimension = 1
The rock has momentum and is thrown in gravity. -> It flies a downwards-curve. Dimension = 2
The rock has momentum and is thrown in gravity and the planet is rotating. -> It flies a downwards-curve and side-ways, due to the coriolis-force. Dimension = 3