A suspension bridge with weight uniformly distributed along its length has twin towers that extend 55 meters above the road surface and are 1600 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 400 meters from the center. (Assume that the road is level.) The height of the cables is meters. www

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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**Suspension Bridge Physics and Mathematics Explanation**

A suspension bridge with uniformly distributed weight along its length includes twin towers extending 55 meters above the road surface. The distance between the towers is 1600 meters. The shape of the suspension cables is parabolic, and they are suspended from the tops of the towers. These cables reach down to touch the road surface at the center point of the bridge. 

**Problem Statement:**

Determine the height of the suspension cables at a location 400 meters away from the bridge’s center. Assume that the road is completely level.

**Calculation Task:**

The objective is to find the height (in meters) of the cables at this specified point. The result should be presented in a simplified form:

"The height of the cables is [___] meters."

(Simplify your answer.)
Transcribed Image Text:**Suspension Bridge Physics and Mathematics Explanation** A suspension bridge with uniformly distributed weight along its length includes twin towers extending 55 meters above the road surface. The distance between the towers is 1600 meters. The shape of the suspension cables is parabolic, and they are suspended from the tops of the towers. These cables reach down to touch the road surface at the center point of the bridge. **Problem Statement:** Determine the height of the suspension cables at a location 400 meters away from the bridge’s center. Assume that the road is completely level. **Calculation Task:** The objective is to find the height (in meters) of the cables at this specified point. The result should be presented in a simplified form: "The height of the cables is [___] meters." (Simplify your answer.)
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