Question

The girder bridge of a railway bridge is in the parabolic form with span 100ft and the highest point on the arch is 10ft above yhe bridge. Find the height of the bridge at 10ft tobthe left or right from the midpoint of the bridge​

Answer 1

Given : The girder bridge of a railway bridge is in the parabolic form with span 100ft and the highest point on the arch is 10ft above the bridge

To find : height of the bridge at 10 ft to the left or right from the midpoint of the bridge​

Soluion:

y = ax² + bx  + c

at x = 0   y = 10

=> c  = 10

y = ax² + bx  + 10

span 100ft

Hence x = 50  & -50   for  y = 0

=> 2500a  + 50b   + 10 = 0

   2500a   - 50b  + 10 = 0

=> 5000a + 20 = 0

=> a  = -20/5000

=>a = -1/250

100b = 0

=> b = 0

y  =  -x²/250   + 10

10 ft  left or right from the midpoint of the bridge​

=> x = -10 or 10

=> y =  - (10)²/250  + 10

=> y = - 100/250 + 10

=> y = 9.6

height of the bridge at 10ft to the left or right from the midpoint of the bridge​ = 9.6 ft

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