Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 90 meters above the road surface and are 800 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 200 meters from the center. ​ (Assume that the road is​ level.) The height of the cables is nothing meters.

Answer 1

y=22.5 m

Step-by-step explanation:

Given that

P (800 , 90)

Shape is parabolic

When x= 200 m we have to find the values of y

We know that equation of parabola

y = a x²

At x= 400 m y= 90 m ( 400 distance from center)

So

90 = 400² a ( 400 distance from center)

a=90/400² = 90/(160000)

y = a x²

y = 90/(160000) x²

When x= 200 m

y = (90 x 200² )/(160000)

y= 90 x 40000/(160000)

y= 90 x 4/(16)

y=22.5 m