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Chapter 10: Q. 73 (page 645)

Parabolic Arch Bridge - A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. See the illustration. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

Short Answer

Expert verified

The height of the arch at distance 10 is 24路31ft ,at distance 30 is role="math" localid="1647070442407" 17路25ftand at distance 50 is 7路64ft .

Step by step solution

01

. Given information .

Consider the given distance and height .

02

Step 2.  Equation of parabola used to find the height of arch .

The equation of parabola is x2=4aythe vertex is at origin and the focus is on the y negative axis .

Here x=1202=60,y=25.

Substitute the values in equation of parabola .

role="math" localid="1647069074022" x2=-4ay602=-4路25路aa=-36

03

Step 3. Find the distance of arch at different distances 10 ,30 ,and 50 feet .

Substitute the value of a and x=10in the equation of parabola.

x2=-4ay102=-36路4yy=-0路69424路31ft

Now at x=30

localid="1647070171631" x2=-4ay302=-36路4yy=-5.84417路25ft

Further simplify .

Substitute x=50in the equation .

localid="1647070205613" x2=-4ay502=-36路4yy=-17.367.63ft

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