Equations of the three parabolas

  • Thread starter Thread starter jrm2002
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around determining the equations of three parabolas based on given graphical information. The original poster seeks to find constants for the parabolic equations but has encountered difficulties due to a lack of numerical labels on the graphs and insufficient data regarding the points of intersection.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for specific spline points where the parabolas meet and suggest matching slopes at these points. There are questions about the lack of numerical data and clarity in the original poster's description of the problem.

Discussion Status

The conversation is ongoing, with some participants offering guidance on how to approach the problem, particularly regarding the need for more information and the correct formulation of the parabolic equations. There is no explicit consensus on the best way to proceed, as multiple interpretations of the problem are being explored.

Contextual Notes

Participants note that the original equations provided by the poster may not be suitable, as they assume the parabolas are centered at zero, which may not align with the actual graphs. The total length of the parabolas and their points of intersection are mentioned, but specific x,y coordinates are still needed for clarity.

jrm2002
Messages
54
Reaction score
0

Homework Statement



Computing the equations of the three parabolas involved

Homework Equations



y=A1x^2 + B1

y= A2x^2+B2

y=A3x^2+B3



The Attempt at a Solution



Tried to get the constants A and B but unsuccessful!


See the attached file for the three parabolas.The dotted points indiacate the change in curvature.
How to get 2 constants in each of the three parabolas?Please help!
 

Attachments

Physics news on Phys.org
Pretty hard to solve for the numbers when there are no number labels on the graphs... Am I missing something?
 
You will need to specify the spline points, that is, where your parabolas meet.

You should also match the slopes at those points.

Next trouble is that you have:

[tex]A_n x^2 + B_n[/tex] where n = 1,2,3
But you need:
[tex]A_n (x - {k_n})^2 + B_n[/tex] where n = 1,2,3
Where the [itex]k_n[/itex] specify the x coordinate of the apex of the parabola.


Matching the slopes seems to requires:
[tex]A_n (x_n- k_n) = A_{n+1}(x_n-k_{n+1})[/tex] for n = 1 2 where [itex]x_n[/itex] is your 2 spline points.

By matching the slopes you will avoid having a corner at the matching point.
 
Last edited:
The total length is 7 metres.
The first parabola meets the second at 0.7 metres.
The second parabola meets the third at 6.3 metres.

As you see,at the points where the parabolas meet, there is a change in curvature
 
Not enough data. What are the x,y points of join?
 
The more information you can provide the easier it will be to help. Currently we are having to guess what it is you are trying to do. Could you please make an effort to actually express what it is you are trying to do. Use more then 3 words in a sentence.

Now, that said, go back and read my last post. Until you get a correct experssion for each of the parabolas there is no way you can arrive at a correct solution. The equations in your original post cannot work. They represent 3 parabolas centered at zero, if I guess correctly NONE of your parabolas have a center at zero.


If you do not want to match slopes at the splines that is your call, just means you do not have those as constraints.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
5K
Replies
3
Views
5K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
2
Views
4K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 9 ·
Replies
9
Views
5K