Suspension Bridge 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. (Assume that the road is level.)
To calculate: The height of the cables, which are suspended from the top of the towers, at a point 100 meters from the centre.
Answer to Problem 13AYU
Solution:
The height of the cable 100 meters from the centre is meters.
Explanation of Solution
Given:
A suspension bridge has twin towers that extend 75 meters above the road and are 400 meters apart. The cables are parabolic in nature and are suspended from the top of the towers. The cables touch the road surface at the centre of the bridge.
Calculation:
Consider the below diagram. The given data can be represented in this diagram.
The line AB is the road which is 400 meters wide.
The lines AD and BC are the twin towers that are 75 meters high.
The cables touch the road at its centre.
The coordinates of the points at the top of the twin towers will be
The cables will form the shape of a parabola, which is of the form .
Thus, now, in order to find the value of , let us use the equation of the parabola.
Thus, considering the point , we get
Therefore, the equation of the parabola is .
Now, we need to find the height of the cable at a point 100 meters from the centre.
Therefore, we have to find the point at .
Thus, we get
Thus, the height of the cable 100 meters from the centre is meters.
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