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Chapter 10: Q. 74 (page 645)

Parabolic Arch Bridge - A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch a distance of 40 feet from the center is to be 10 feet. Find the height of the arch at its center.

Short Answer

Expert verified

The height of the arch at its center is nearly 28 ft .

Step by step solution

01

Step 1. Given information .

Consider the given distance and height .

02

Step 2. Standard form of parabola used .

The standard form of parabola isx-h2=4ay-k.

03

Step 3. Find the height  .

Using the standard form of parabola .

Substitute the values x=40,y=10andh=0in the equation of parabola .

role="math" localid="1647071687110" 40-02=4a10-k1600=40a-4ak

Now ,substitute x=50,y=0

50-02=4a0-k2500=4ak

After comparing both equations the value ofa=-452=-22路528ft

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