Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 75 meters above the road surface and are 400 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 100 meters from the center.

Answer 1

Answer:

Let take the center of bridge as our origin (0,0). Parabola having vertex at origin is represented by y=a.x^2

At the right far end or +ive x-axis side we've x=200 and y=75 , so a=75/(200^2)=0.001875

Y

Parabola equation y=0.001875*x^2

Height of cable from 100m from centre. Y=? ,X=100m

Y=0.001875*(100^2)

Y=18.75 m

Height of ropes at 100m from the center of bridge.

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