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Chapter 10: Q. 68 (page 644)

Suspension Bridge - The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?

Short Answer

Expert verified

The height of the cable at a point 50 feet from the center is 15.625 ft .

Step by step solution

01

Step 1. Given information .

Consider the given distance from the base and height .

02

Step 2. Standard form of parabola used .

The standard form of parabola is x2=4aythe vertex of the parabola is at origin and focus is on the y positive axis .

03

Step 3. Find the height of cable .

To find the height of the cable substitute the value of a in the standard form of parabola .

Here x=4002=200,y=100-10=90

localid="1647073157267" x2=4ay2002=4a路90a=111路11

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1647073166393" x2=4ay502=4路111路11yy=15路625ft

Therefore the height of cable from the center of bridge islocalid="1647073173934" 15路625ft.

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