Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 95 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. ​ (Assume that the road is​ level.)

Answer 1

Answer:

Height = 23.75 metres

Step-by-step explanation:

The Twin Towers are 1200 metres apart. This means that the centre point of the two towers is

1200/2 = 600metres

Since the cables are parabolic in shape, we will use the parabola equation

y = ax^2

y = 95 metres

x = 600 metres

Put x and y into the equation. We have

95 = a(600)^2

a = 95/600^2

a = 95/ 360000

a = 19/72000

Therefore, y = (19/72000)x^2

To find the height of the cable at 300 metres from the center, it means x is now equal 300 metres

Recall that

y = (19/72000)x^2

y = (19/72000)300^2

y = (19*300*300)/72000

y = (19*90000)/72000

y = 23.75

The height is 23.75 metres