|
Question 1157836: A suspension bridge with weight uniformly distributed along its length has twin towers that extend 100 meters above the road surface and are 800 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 200 meters from the center.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Let the vertex be at the point ( 0, 0 )
The parabolic cables are connected
to towers at ( 400, 100 ) and ( -400, 100 )
-----------------------
You need to find  at points
( 200, y[1] ) and ( -200, y[1] )
-----------------------
The form is:
At ( 0, 0 )
At ( 400, 100 )
(1) 
At ( -400, 100 )
(2) 
---------------------------
Add (1)and (2)
(1)
(2)
-----------------------------
and
(1)
(1) 
(1) 
(1) 
--------------------
The equation is:
At ( 200, y[1] )
( you get the same result at ( -200, y[1] ) )
The height of the cables at a point
200 meters from the center is 25 m
---------------
check the math & get a 2nd opinion if needed
-------------------------------------------
|
|
|
| |
