Parabola Word Problem

• April 3rd 2006, 04:59 AM
OverclockerR520
Parabola Word Problem
Hello,

This is only my 3rd post here I'm pretty sure. I want to say thanks again to those who helped me with my first post in the two questions I listed. I have another question on how to set up this word problem which is based off a parabola. I was told to that an x axis and y axis can be found after making a scetch of the bridge in the below problem but I couldnt understand how if the bridge is rectangular.

4) One section of a suspension bridge has its weight uniformly distributed between two towers that are 400 feet apart and rise 90 feet above the horizontal roadway (see figure). A cable strung between the tops of the towers has the shape of a parabola, and its center point is 10 feet above the roadway. Suppose coordinate axes are introduced as shown in the figure.

a) Find the equation for the parabola.

b) Nine equally spaced vertical cables are used to support the bridge. Find the total length of these supports.
• April 3rd 2006, 07:57 AM
earboth
Quote:

Originally Posted by OverclockerR520
...
4) One section of a suspension bridge has its weight uniformly distributed between two towers that are 400 feet apart and rise 90 feet above the horizontal roadway (see figure).

Hello,

please provide me with the above mentioned figure and I'll give you some help. Promised!

Greetings

EB
• April 3rd 2006, 12:10 PM
earboth
Quote:

Originally Posted by OverclockerR520
4) One section of a suspension bridge has its weight uniformly distributed between two towers that are 400 feet apart and rise 90 feet above the horizontal roadway (see figure). A cable strung between the tops of the towers has the shape of a parabola, and its center point is 10 feet above the roadway. Suppose coordinate axes are introduced as shown in the figure.

a) Find the equation for the parabola.

b) Nine equally spaced vertical cables are used to support the bridge. Find the total length of these supports.

Hello,

I'm going to show you what I've figured out without a figure:
1. I've attached a diagram about the situation as I understand it.

2. The form of the cable ist described by a parabola, where the Vertex is V(0, 10). The roadway lies exactly on the x-Axis. So the equation of the parabola has the form:
$y=p(x)=a\cdot x^2 + c$
Therefore c = 10. Sub in the coordinates of the top of the right tower T(200, 90) and you'll get;
$90=p(200)=a\cdot 200^2 + 10$. Solve for a and you get the complete equation:
$p(x)=\frac{1}{500} \cdot x^2 + 10$

3. With 9 vertical cables you've got 10 equidistant parts, that means each part has the width of 40'. The total length of all vertical cables consist of:
L(cables)=10 + 2*p(40) + 2*p(80) + 2*p(120) + 2*p(160) = 286'.

By the way: A cable which hangs between two points doesn't form a parabola, but a curve which is called catenary (literally translated it means: curve of a (hanging) chain)

Greetings

EB
• April 4th 2006, 09:16 PM
OverclockerR520
Got The Information
Hey,

Thanks for that reply and the diagram you came up with is basically the same diagram in the problem. Sorry it took so long to reply Ive been busy studying for mid terms and doing some half year projects. This forum is a real big help on a serious note. But back ontopic, as you requested, problem 1 and problem 4 with the correct diagrams, hope this helps.

Problem 1 with diagram = http://putfile.com/pic.php?pic=4/9323142814.jpg&s=x10

Problem 4 Bridge Diagram =
http://putfile.com/pic.php?pic=4/9323154362.jpg&s=x10

Any help much appreciated, thanks! :)
• April 5th 2006, 01:15 AM
earboth
Quote:

Originally Posted by OverclockerR520
Hey,
But back ontopic, as you requested, problem 1 and problem 4 with the correct diagrams, hope this helps.
Problem 1 with diagram = http://putfile.com/pic.php?pic=4/9323142814.jpg&s=x10
Problem 4 Bridge Diagram =
http://putfile.com/pic.php?pic=4/9323154362.jpg&s=x10

Any help much appreciated, thanks! :)

Hello,

to 1.: You know the zeros of your function. x = 2 is a "double" zero, because the x-Axis is tangent to the curve. So your function has the equation
$f(x)=a \cdot (x-2)^2 (x-4)$
Sub in the coordinates of point A to calculate the coefficient a:
$-3=a \cdot (1-2)^2 (1-4)$ and solve for a. You'll come up with a = 1.
$f(x)=(x-2)^2 (x-4) = x^3-8x^2+20x-16$