Question

What is the height of the cable at a point 150 feet from the center of the bridge?

Answer 1

The cable is 10 feet from the road surface 150 ft from the center of the bridge

Explanation:

This is a parabola that opens up and has vertex at the origin (0,0), so the equation is: x² = 4ay

First find a using a known point (300, 40):

x = 600/2 = 300 (half the length of the span; distance from center to the end)

y = 40 height where cable is tied at the end

300² = 4a(40)

a = 90,000/160 = 562.5

Now find y, 150 ft right of center:

150² = 4(562.5)y

y = 150²/2250 = 10 ft

Answer 2

The cable is 30 feet from the road surface at a point 150 feet from the center of the bridge.