Word Problem

Question

The towers of a suspension bridge are 800 feet apart and rise 162 feet higher than the road. Suppose that the cable between the towers has the shape of a parabola and is two feet higher than the road at the halfway point between the towers. What is the approximate height of the cable 120 feet from either tower?

I need the steps along with the answer to this problem pleasee

Answer 1

Hi Elizabeth,

 

The low point of the cable will be the vertex of the parabola

 

the low point is (0,2)   and then the towers are 400 feet to the left and right

 

so we have the vertex and a point and that will help us find the equation of the parabola

 

y = a(x-h)² + k  (this is the equation of the parabola and (0,2) are h and k

 

y = a(x-0)² + 2

 

now lets put in one of the other points and solve for a, we will use the point (400,162)  this is the right tower

 

162 = a(400)² +2 

 

160 = a(400)²

 

160 = 160000a

 

a = 1/1000

 

so our equation is

 

y = 1/1000*x² + 2

 

now the x value of a point 120 ft from the right tower would be 400 - 120 = 280

 

substitute this in the equation

 

y = 1/1000*(280)² + 2

 

y = 78.4 + 2

 

y = 80.4 feet 

 

hope this helps