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Solved: (See the Guided Projects for additional
Chapter 9, Problem 84E(choose chapter or problem)
(See the Guided Projects for additional applications of conic sections.)
Golden Gate Bridge Completed in 1937, San Francisco’s Golden Gate Bridge is 2.7 km long and weighs about 890,000 tons. The length of the span between the two central towers is 1280 m; the towers themselves extend 152 m above the roadway. The cables that support the deck of the bridge between the two towers hang in a parabola (see figure). Assuming the origin is midway between the towers on the deck of the bridge, find an equation that describes the cables. How long is a guy wire that hangs vertically from the cables to the roadway 500 m from the center of the bridge?
Questions & Answers
QUESTION:
(See the Guided Projects for additional applications of conic sections.)
Golden Gate Bridge Completed in 1937, San Francisco’s Golden Gate Bridge is 2.7 km long and weighs about 890,000 tons. The length of the span between the two central towers is 1280 m; the towers themselves extend 152 m above the roadway. The cables that support the deck of the bridge between the two towers hang in a parabola (see figure). Assuming the origin is midway between the towers on the deck of the bridge, find an equation that describes the cables. How long is a guy wire that hangs vertically from the cables to the roadway 500 m from the center of the bridge?
ANSWER:
Solution 84E
Step 1 of 2:
The given figure is shown below ;
Clearly , the given figure represents a parabola open up wards , and ( 640, 152) lies on the parabola .
We know that , the equation of a parabola open up wards with vertex at origin is :
Hence , ( 640, 152) lies on the parabola
=
4a 2694.7368
Therefore , equation of the cable is :
That is , or
…………(1)