Grade 11 Precalculus

Question

The towers supporting the cable of a suspension bridge are 100 m apart and 30 m above the bridge it supports. Supposedly, the cable hangs, following the shape of a parabola, with its low est point 5 m above the bridge. How high is the cable 40 m away from the center? Show your solutions and illustrations.

Answer 1

Think of the base of one of the towers as the point (0,0)

The top of that tower where the cable is would have the point (0,30)

the top of the tower 100 m apart would have the point (100,30)

the cable having a parabolic shape would have a vertex between those two points at (50,5)

*The y coordinate of each of these points would represent the height above the bridge.

With the vertex point and the point of the top of either of the towers would produce the equation

h(x)= 0.01(x-50)²+5

The height of the cable 40 m away from the center would either be at the point 50-40 or 50+40 / 10 or 90

h(10) = 21

&

h(90) = 21

The height of the cable 40 m away from the center would be 21 m above the bridge