- #1

XtinaVoiceWithin

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2. What has only magnitude?

( is it scalar, vector, frame of reference)

3. What is the path of a projectile? (hyberbole or parabola)

Sorry if this question is kind of unclear.

Thanks !

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- Thread starter XtinaVoiceWithin
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- #1

XtinaVoiceWithin

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2. What has only magnitude?

( is it scalar, vector, frame of reference)

3. What is the path of a projectile? (hyberbole or parabola)

Sorry if this question is kind of unclear.

Thanks !

- #2

Zhou Yu

- 11

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2. If is only magnitude then it would be scalar.

3. When you say projectile, I am thinking something like a arrow being shot into the air and then travels in an arc of some kind.

In which case that would make it a Parabola.

A hyperbole is like a parabola except rotated 90 degrees.

- #3

Ambitwistor

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A hyperbola is not a rotated parabola.

- #4

Zhou Yu

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However Ambitwistor, is right in saying that "A hyperbola is not a rotated parabola".

However I did say it is "like" a parabola, but having done a little more research into it, a parabola isn't really like a hyperbola at all.

____________________________________________________________

A hyperbola is the set of all points P(x,y) in the plane such that

| PF1 - PF2 | = 2a

Both F1 and F2 are focus points, and the difference between them is always the same.

A hyperbola also has asymptotes which are the boundaries of the hyperbola. A parabola however does not have such boundaries.

Also a Hyperbola is where there are two curves, and F1 - F2 will always equal a constant of 2a.

A Parabola only consists of 1 line.

____________________________________________________________

I hope this compensates a little for my mistake about the difference between a parabola and a hyperbola.

- #5

Integral

Staff Emeritus

Science Advisor

Gold Member

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y = (x-h)

This is arc of a projectile, it is created by slicing a cone by plane not parallel to the axis but intersecting the base of the cone.

A hyperbola is described by

(x-h)

This is created by slicing a cone in a plane parallel to the main axis. It is charaterized by 2 non connected pieces.

This is the path followed by a body moving in space which passes near a massive body but is not in an orbit around the body.

- #6

XtinaVoiceWithin

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Thanks so much for putting so much effort to my questions.

- #7

Gale

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- #8

Ambitwistor

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Originally posted by Gale17

I think I know what you're thinking, but you have it a little garbled.

First, by "oval" I'm guessing you mean an ellipse. It's true that if you throw an object, it follows an elliptical orbit (if you throw it at less than escape velocity). A partial arc of an ellipse is not a parabola. (i.e., if you cut a piece off an ellipse, the piece is never a parabola.) However, over a small distance, an arc of an ellipse is well approximated by a parabola -- they're very similar in shape.

So, we say that if you throw a ball, it follows a parabolic arc. But it's really following part of an elliptical arc that, over a comparatively small distance, is very similar to (but not the same as) a parabola.

- #9

Gale

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- #10

Ambitwistor

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Originally posted by Gale17

heh... i actually sat for like 5 minutes trying to figure out the other word for oval...

Maybe it's "walltet".

- #11

Gale

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Maybe it's "walltet".

OOOOOH! hahaha... you're a clever one aren't you... yeah... so I'm not so great with english... pfft, its only my native language...

- #12

russ_watters

Mentor

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Another way to think of it is circles and parabolas are special cases of ellipses. A circle is an ellipse with zero distance between the foci and a parabola is an ellipse with infinite distance between the foci. That is why over small distances a parabola and ellipse are very close - they are siblings (conic sections).Originally posted by Ambitwistor

It's true that if you throw an object, it follows an elliptical orbit (if you throw it at less than escape velocity). A partial arc of an ellipse is not a parabola. (i.e., if you cut a piece off an ellipse, the piece is never a parabola.) However, over a small distance, an arc of an ellipse is well approximated by a parabola -- they're very similar in shape.

- #13

Ambitwistor

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Originally posted by russ_watters

Another way to think of it is circles and parabolas are special cases of ellipses. A circle is an ellipse with zero distance between the foci and a parabola is an ellipse with infinite distance between the foci. That is why over small distances a parabola and ellipse are very close - they are siblings (conic sections).

Not really. It's true that parabolas and ellipses are conic sections with the properties you note. But the reason why a small arc of an ellipse looks like a parabola has nothing to do with the fact that they are both conic sections.

In fact, any trajectory due to any force law -- not just conic section solutions to an inverse square law -- will look like a parabola over small distances. This is a consequence of Taylor's theorem, expanding to second order. It arises because any gravitational field locally looks like a uniform field over a distance scale smaller than the scale of its gradient, and a parabola is the trajectory obtained from a uniform field.

- #14

Chi Meson

Science Advisor

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- #15

PhalanxGun

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