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Chapter 3: Q. 27 (page 174)

Parabolic Arch Bridge A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure, what is the height h of the arch 2 feet from shore?

Short Answer

Expert verified

The height is3.6unit.

Step by step solution

01

Step 1. Given information.

Parabolic Arch Bridge A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure, what is the height h of the arch 2 feet from shore?

02

Step 2. Equation of parabola.

The goal of this task is to find the coordinates of the points on the parabola.

The equation of parabola is given by:

y=a(x-h)2+k

where h,kare the coordinates of the vertex.

03

Step 3. Find the height.

It is clear from the figure that the vertex has coordinates 0,10, the point 10,0is on the parabola, too. Find a.

Here

h,k=0,10x,y=10,0

So,

y=ax-h2+k0=a10-02+100=100a+10a=-10100=-0.1

Equation of parabola is:

y=-0.1x2+10

To find y-coordinate of the point, put x=8in the equation:

y=-0.1x2+10y=-0.1(8)2+10y=-0.164+10y=-6.4+10y=3.6

The height is 3.6unit.

04

Step 4. Conclusion.

The height is 3.6 unit.

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