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Unread 17-02-2014, 11:57
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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.



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Unread 17-02-2014, 16:25
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Re: Math Quiz: Parabola Path



Hint: the answer is not

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

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Unread 17-02-2014, 18:08
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Re: Math Quiz: Parabola Path

I get:

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

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

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Unread 17-02-2014, 18:29
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by Qbot2640 View Post
I get:

Bottom curve: y = -.0433x^2 - 1
Not. See my previous post.

Quote:
Originally Posted by Qbot2640 View Post
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.


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Unread 17-02-2014, 18:40
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by Ether View Post
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).
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Unread 17-02-2014, 19:16
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by Qbot2640 View Post
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.


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Unread 17-02-2014, 19:24
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by Ether View Post
Hint#2: the top and bottom boundary curves are not true quadratics.
Graph of upper and lower boundary curves
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Unread 02-03-2014, 20:40
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Re: Math Quiz: Parabola Path


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

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Unread 03-03-2014, 00:02
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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)
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Unread 03-03-2014, 09:51
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by RyanCahoon View Post
Can I give the answers in parametric form?
You got it

Reps to you !


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Unread 06-03-2014, 17:57
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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 ?


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Unread 11-03-2014, 16:45
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by Ether View Post
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?


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Unread 11-03-2014, 18:32
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Re: Math Quiz: Parabola Path

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Originally Posted by Ether View Post
Does anyone have access to Mathematica?
http://www.wolfram.com/mathematica/trial/
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Unread 11-03-2014, 18:44
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Re: Math Quiz: Parabola Path

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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?


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Unread 11-03-2014, 20:07
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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.
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