Chief Delphi

Chief Delphi (http://www.chiefdelphi.com/forums/index.php)
-   Math and Science (http://www.chiefdelphi.com/forums/forumdisplay.php?f=70)
-   -   Math Quiz: Parabola Path (http://www.chiefdelphi.com/forums/showthread.php?t=126639)

Ether 17-02-2014 11:57

Math Quiz: Parabola Path
 


The center of a circle of radius=1 traverses the parabolic trajectory.. y = -0.0433*x2.. from x=-5 to x=+5 in the XY plane, and as it does so it "sweeps out" a path with upper and lower boundaries.

Find the equations for the upper and lower boundary curves.




Ether 17-02-2014 16:25

Re: Math Quiz: Parabola Path
 
1 Attachment(s)


Hint: the answer is not

Code:

y = -0.0433*x2 + 1
and
y = -0.0433*x2 - 1



Qbot2640 17-02-2014 18:08

Re: Math Quiz: Parabola Path
 
I get:

Top curve: y = -0351x^2 + 1

Bottom curve: y = -.0433x^2 - 1


Ether 17-02-2014 18:29

Re: Math Quiz: Parabola Path
 
1 Attachment(s)
Quote:

Originally Posted by Qbot2640 (Post 1344773)
I get:

Bottom curve: y = -.0433x^2 - 1

Not. See my previous post.

Quote:

Originally Posted by Qbot2640 (Post 1344773)
I get:

Top curve: y = -0351x^2 + 1

I assume there's supposed to be a decimal point before the "0".

Nice try, but no cigar.



Qbot2640 17-02-2014 18:40

Re: Math Quiz: Parabola Path
 
Quote:

Originally Posted by Ether (Post 1344785)
Not. See my previous post.



I assume there's supposed to be a decimal point before the "0".

Nice try, but no cigar.



My mistake...I had all three equations together, and grabbed your original as the "bottom". The top I got (as you corrected my missing decimal) is 0.0351x^2 + 1

The bottom I got was 0.0474x^2 -1

I calculated two normal lines and found points that were 1 unit away from points on your given original. Then calculated the quadratics from the two sets of three points (although the y intercepts being known, one really only needs two points).

Ether 17-02-2014 19:16

Re: Math Quiz: Parabola Path
 
1 Attachment(s)
Quote:

Originally Posted by Qbot2640 (Post 1344796)
My mistake...I had all three equations together, and grabbed your original as the "bottom". The top I got (as you corrected my missing decimal) is 0.0351x^2 + 1

The bottom I got was 0.0474x^2 -1

The top equation y = -0.0351x^2 + 1 is still not right (even with the required "-" sign added back in :))

The bottom equation y = -0.0474x^2 - 1 (with the "-" sign added) is a very good approximation in the given range, but as you can see in the attached graph, it diverges outside that range.

Quote:

I calculated two normal lines and found points that were 1 unit away from points on your given original.
You've got the right general idea.


Quote:

Then calculated the quadratics...
Hint#2: the top and bottom boundary curves are not true quadratics.



Ether 17-02-2014 19:24

Re: Math Quiz: Parabola Path
 
1 Attachment(s)
Quote:

Originally Posted by Ether (Post 1344818)
Hint#2: the top and bottom boundary curves are not true quadratics.

Graph of upper and lower boundary curves

Ether 02-03-2014 20:40

Re: Math Quiz: Parabola Path
 

Any math/physics teachers want to give this a try?


RyanCahoon 03-03-2014 00:02

Re: Math Quiz: Parabola Path
 
Can I give the answers in parametric form?

Spoiler for parametric plot equations:
xlower(t) = t - 0.0866 t / √(1 + (0.0866 t)2)
ylower(t) = -0.0433 t2 - 1 / √(1 + (0.0866 t)2)

xupper(t) = t + 0.0866 t / √(1 + (0.0866 t)2)
yupper(t) = -0.0433 t2 + 1 / √(1 + (0.0866 t)2)

Ether 03-03-2014 09:51

Re: Math Quiz: Parabola Path
 
Quote:

Originally Posted by RyanCahoon (Post 1352377)
Can I give the answers in parametric form?

You got it:)

Reps to you !



Ether 06-03-2014 17:57

Re: Math Quiz: Parabola Path
 

Is it possible to represent Ryan's parametric equations in explicit form y=f(x) ?

Or even implicit f(x,y)=0 ?



Ether 11-03-2014 16:45

Re: Math Quiz: Parabola Path
 
Quote:

Originally Posted by Ether (Post 1354695)
Is it possible to represent Ryan's parametric equations in explicit form y=f(x) ?

Or even implicit f(x,y)=0 ?

Does anyone have access to Mathematica?



cgmv123 11-03-2014 18:32

Re: Math Quiz: Parabola Path
 
Quote:

Originally Posted by Ether (Post 1357532)
Does anyone have access to Mathematica?

http://www.wolfram.com/mathematica/trial/

Ether 11-03-2014 18:44

Re: Math Quiz: Parabola Path
 
Quote:

Originally Posted by cgmv123 (Post 1357611)

Thank you, I am aware of that. For a variety of reasons, I don't install or use trial software.

Are there any Mathematica gurus out there in CD land?



maths222 11-03-2014 20:07

Re: Math Quiz: Parabola Path
 
As a function of x, it will describe the upper boundary on one side and the lower on the other. It does exist, but it is very ugly. I will try to remember to post it later.


All times are GMT -5. The time now is 12:03.

Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © Chief Delphi