Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 65 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:

16.25 m

Explanation:

we know that the equation pf parabola

$y=kx^2$

from bellow figure the coordinate of parabola is (600,65) that is y=600 and x=65

putting the the value of y and x in the equation of parabola

$65=k600^2$

k=0.0001805

now the equation is

$y=0.0001805x^2$

we have to find the value of y at x=300m

so $y=0.0001805\times 300^2$

y=16.25 m