[MOVED] Can the truck fit through the tunnel?

coke0011

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Nov 21, 2006
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There is a tunnel in the shape of a semi-ellipse. The tunnel is 14 feet tall and 30 feet wide at ground level. A truck is 13 feet tall and 10 feet wide. Will the truck make it through the tunnel?

I found that the answer was no and that the tunnel is only 8 feet wide at the point where the truck is 10 feet wide. Can someone check the work for me? Thanks so much.
 
coke0011 said:
Can someone check the work for me?
Gladly. But you'll need to post that work, first.

Thank you.

Eliz.
 
Why does the truck have to stay on one side of the road?

Can't you drive down the middle so that the sides of the truck are only 5' from the center?
 
I created a parabola to be used a scale model for the tunnel. The parabola is y=-.062X^2. When you put -1 in for Y (Showing what the width is at 13 ft., the X value is +/- 4. This means that the tunnel is 8 feet wide at this point when it would have to be 10 for the truck to fit. To get the equation of the parabola i just did a vertical shrink. Normally an X value of 15 would give -225 in this equation but i need it to be -14 to fit the dimensions of the tunnel so i just did -14/-225 to get -.062.
 
coke0011 said:
I created a parabola...
You lost me right there. All that other writing is not meaningful.

There is a tunnel in the shape of a semi-ellipse.
Why on Earth would you use a parabola?
 
Hello, coke0011!

Are you familiar with ellipses at all?


There is a tunnel in the shape of a semi-ellipse.
The tunnel is 14 feet tall and 30 feet wide at ground level.
A truck is 13 feet tall and 10 feet wide.
Will the truck make it through the tunnel?
Code:
               *  *  *
          *       :       *
        *         :         *
       *        14:          *
                  :
      *           :           *
    --*-----------+-----------*--
                        15

You're expected to know that the ellipse with \(\displaystyle a\,=\,15,\:b\,=\,14\) is:

. . . \(\displaystyle \L\frac{x^2}{225} \,+\,\frac{y^2}{196}\:=\:1\;\;\Rightarrow\;\;y \:=\:\frac{14}{15}\sqrt{225\,-\,x^2}\)


The truck is 10 feet wide and 13 feet high.
Driving down the middle of the tunnel, it looks like this:
Code:
               *  *  *
          *---------------*
        * |       :       | *
       *  |       :      y|  *
          |       :       |
      *   |       :       |   *
    --*---+-------+-------+---*--
                      5

Is there enough clearance?

When \(\displaystyle x\,=\,5:\;y\:=\:\frac{14}{15}\sqrt{225-5^2} \;=\;\frac{14}{15}\sqrt{200} \:\approx\:13.2\) feet

Yes, the 13-foot truck will make it through . . . with a good driver.
. . (There is less than 7 inches clearance on each side.)

 
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