Answer to Question #255563 in Analytic Geometry for Joshua

Question

2. The recently made suspension bridge cables in New Bataan Hydro plant are in the shape of a parabola. The distance between two towers supporting the cable are 800 feet apart and the height is 200 feet. If the vertical support cables are at 100 feet intervals along the level roadway, what are the lengths of these vertical cables?

Answer 1

Let $y(x)=ax^2$be the equation of the parabola, $a>0.$

The distance between two towers supporting the cable are 800 feet apart and the height is 200 feet

$$y(-400)=y(400)=200$$

$$a(-400)^2=a(400)^2=200$$

$$a=0.00125$$

Then the equation of the parabola is

$$y(x)=0.00125x^2$$

$$y(-300)=y(300)=0.00125(300)^2=112.5$$

$$y(-200)=y(200)=0.00125(200)^2=50$$

$$y(-100)=y(100)=0.00125(100)^2=12.5$$

$112.5\ ft, 50\ ft, 12.5\ ft,$ and $12.5 \ ft, 50\ ft, 112.5\ ft.$