|
Question 1185542: The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet and 80 feet high, with the cables touching the road surface midway between the towers.
a.) Find the equation of the shape of the cable
b.) What is the height of the cable from the road at a point 150 ft from the center of the bridge
c.) Using the equation from part a, determine the total length of cable needed for the vertical sections of the cables spaced 20-foot interval.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A similar problem:
----
A cable suspended between two posts that are the same height and 20 meters apart has a sag of 1 1/2 meter. If the cable hangs in the form of a parabola, find its equation, taking the lowest point as the origin.
---------------------
3 points on the parabola are:
(-10,1.5), (0,0), (10,1.5)
---
A parabola has the form y = ax^2 + bx + c
Sub the values and solve for a, b & c.
Do the (0,0) first:
0 = a*0 + b*0 + c ---> c = 0
----
For (-10,1.5):
1.5 = a*100 - 10b
For (10,1.5):
1.5 = a*100 + 10b
1.5 = a*100 - 10b
--------------------- Subtract
0 = 20b
b = 0
==================
1.5 = a*100 + 10b
1.5 = a*100 - 10b
-----------------------Add
3 = 200a
a = 3/200
-------------
y = (3/200)x^2 is the parabola
|
|
|
| |
