A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below. http://prntscr.com/80crs3 What is the vertical clearance 2 m from the edge of the tunnel?

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A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below. http://prntscr.com/80crs3 What is the vertical clearance 2 m from the edge of the tunnel?

Mathematics
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  • phi
I would find the equation of the parabola, then use that equation with x=8 (which is 2 m from the edge at x=10)
  • phi
the zeros of this parabola are at x=10 and x=-10 (with x=0 the middle of the parbola) in other words, y = a(x-10)(x+10) where we still need to find a luckily we know when x=0 the parabola has height 50 (i.e. y=50) so put in x=0 and y=50: 50 = a(-10)(+10) 50 = a* -100 divide both sides by -100 -1/2 = a and the equation is \[ y= - \frac{1}{2} (x-10)(x+10) \]
  • phi
After posting all of that , I see the zeros are at x=5 and x=-5 oops. but hopefully you can redo the work and get the correct equation?? the zeros of this parabola are at x=5and x=-5 (with x=0 the middle of the parbola) in other words, y = a(x-5)(x+5) where we still need to find a

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a= -2
  • phi
yes, and the equation is y = -2 (x-5)(x+5) and 2 meters in from the edge (at x=5) would be x=3 (or x=-3) so put in x= 3 into the equation and find y
y=32
  • phi
that is what I got.
So is that the answer?
  • phi
yes
thanks :)

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