SOLUTION: The towers of a suspension bridge are 800 m apart and are 180 m high. The cable between the towers hangs in the shape of parabola, which at its lowest just touches the road. How hi
Algebra ->
Quadratic-relations-and-conic-sections
-> SOLUTION: The towers of a suspension bridge are 800 m apart and are 180 m high. The cable between the towers hangs in the shape of parabola, which at its lowest just touches the road. How hi
Log On
Question 1183793: The towers of a suspension bridge are 800 m apart and are 180 m high. The cable between the towers hangs in the shape of parabola, which at its lowest just touches the road. How high above the road is the cable 300 m away from the center? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52796) (Show Source):
You can put this solution on YOUR website! .
The towers of a suspension bridge are 800 m apart and are 180 m high.
The cable between the towers hangs in the shape of parabola, which at its lowest
just touches the road. How high above the road is the cable 300 m away from the center?
~~~~~~~~~~~~~~~
Place the origin of the coordinate system at the bridge level, half way between the towers.
Write the parabola equation in vertex form y = ax^2 (in this form the cable touches the road at the origin of the coordinate system).
You are given that y = 180 meters at x = 400 meters.
So you substitute these values into the parabola equation
180 = a*400^2.
From the equation, you find a = = 0.001125.
Thus your parabola is y = 0.001125*x^2.
Now, to answer the problem question, you substitute x= 300 into the last equation
y = 0.001125*300^2 = 101.25 meters. ANSWER
The solution from the other tutor is a perfectly good formal solution by finding the equation of the parabola.
There is no need to find the equation exactly; the answer can be obtained in moments informally.
From the center of the bridge to each end is 400m; we want to find the height 300m from the center of the bridge.
Since the cable is in the shape of a parabola with its vertex at the center of the bridge, the height of the cable 3/4 of the way from the center of the bridge to each tower is the height of the tower, multiplied by (3/4)^2.
