Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 9090 meters above the road surface and are 16001600 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 400400 meters from the center. ​ (Assume that the road is​ level.)

Answer 1

y = 22.5 m

Explanation:

given,

length of the tower = 90 m

distance between the towers = 1600 m

height of cable at 400 m = ?

we know

y = a x²

x is the distance from the center where the cable is touching the ground

at the far end y = 90 m and x = 800

90 = a × 800²

`a = (9)/(64000)`

`f(x) = (9)/(64000)x^2`

now height at x = 400

`y = (9)/(64000)(400)^2`

y = 22.5 m

height of the cables at 400 m is equal to y = 22.5 m