Question

5. The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 150 feet from the center of the bridge? (5 points)

Could you please show how you did your work? Thank you!

Answer 1

Since the cables touch the road surface midway between the towers, this implies vertex is (0,0)

Coordinates of one of the pillars is (300, 80)

The equation of the parabola with vertex at origin is given by

x² = 4py

Given, when x = 300, y = 80

Therefore,

(300)² = 4p(80)

=> p = 90000 / 320

=> p = 281.25

Therefore,

x² = 4(281.25)y

=> x² = 1125y

Now, we need to find the find the value of y when x = 150 feet

Therefore,

(150)² = 1125y

=> y = (150)² / 1125

=> y = 20 feet

Thus,

Height of the cable at a point 150 feet from the center of the bridge is 20 feet