Question 1169290: A railway bridge over a road is in the shape of a parabola.
The bridge is 3m high in the middle and 8m wide at its base.
A truck that is 2.5 m wide is approaching and will pass under the bridge directly through the middle.
What is the maximum height that the truck can have and still pass under the bridge?
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
Graph your concave down parabola with the vertex at the origin. Since it is 3 m high, the bottom must be at -3, and since it is 8 meters wide centered on the vertical axis, it must extend from -4 to 4 at the bottom. That gives us three points, sufficient to define a parabola. Putting the vertex at the origin eliminates the constant and first degree terms, simplifying the function considerably.
The points are ) , ) , and ) , so if any parabola with a vertical axis can be modeled by  , we know that, for this parabola:
Solve the 3X3 system for the coefficients of the desired function. Hint:  and  will both be zero as a consequence of placing the vertex at the origin.
Once you have the desired function, calculate the value of the function at one-half the width of the truck, then subtract this value from 3 meters to find the maximum height of the truck.
John
My calculator said it, I believe it, that settles it
From
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Answer by ikleyn(52797)  (Show Source):
You can put this solution on YOUR website! .
Never saw a railway bridge in the shape of a parabola.
Had such a bridge be ever exist, the design and the construction engineers would lose their licenses next day,
and the bridge would be destroyed.
Or preserved as a monument of a human stupidity . . . with forbiddance to move across it . . .
/\/\/\/\/\/\/\/
In connection with this post, I re-call the old anecdotic story, that was popular among mature construction engineers long time ago.
At the meeting of construction engineers, they are going to discuss on how to construct one particular bridge.
A chief engineer, who conducts the meeting, proposes to the members to out speak their ideas.
One person of the staff takes a word and says: "Hmmm . . . , I propose to construct a bridge across the river".
A silence during next 7 seconds - - - then a curtain . . .
The same (the similar) anecdotic story does exist about construction engineers that are going to build a dam . . . across a river . . .
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