Question

A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.

Image Attached Below

What is the vertical clearance 2 m from the edge of the tunnel?
Answer Choices:
2 m

14.9 m

29 m

16.1 m

Answer 1

do you know what a "vertical clearance" is?

Answer 2

@jdoe0001 no

Answer 3

Find the equation of a parabola, y(x), using your givens. Here y is height and x is distance from center of the parabola. Then find y(6.5 - 2) for your answer.

Answer 4

I'm sorry, I don't understand.

Answer 5

hmm onlyoneze do you drive a car?

Answer 6

yes

Answer 7

Am I suppose to multiply 31 which is y by 4.5?

Answer 8

well. http://onlinesigns.biz/wp-content/uploads/2011/08/Clearance-Sign.png <--- doe that look familiar?

Answer 9

that's what's meant by "vertical clearance"

Answer 10

What is the vertical clearance 2 m \(\bf \color{red}{from}\) the edge of the tunnel?

Answer 11

If you were to go 2 m from the side of the tunnel and look up (from the ground), how high would the ceiling be at that point? That's the clearance.

You know the equation of a parabola is \(x^2 = -4py\implies y(x)=\cfrac{-x^2}{4p}\ \ \), where p is the directix.

To find p, you can use \(y(6.5)=-31=\cfrac{-(6.5)^2}{4p}\).

Once you've got p, to find clearance, you can use \(y(6.5-2)=-31=\cfrac{-(4.5)^2}{4p}\).

http://en.wikipedia.org/wiki/Parabola

Answer 12

http://www.oregon.gov/ODOT/CS/ssb/images/tunnels/toothrock.jpg better example, a tunnel shaped like a parabola

Answer 13

@ybarrap is p .34?

Answer 14

so would the vertical clearance be 5.5? @jdoe0001

Answer 15

Wait, wouldn't it just be 29m?

Answer 16

31-2?

Answer 17

Check your calculations, the rest is easy.

Answer 18

You are on the right track, question I have do you understand what we did?

Answer 19

I understand that the vertical clearance is that distance from the highest point, correct?

Answer 20

what you're being asked is

to be honest I didn't quite get the wording heheh, I thought it was 29 =)

anyhow, what you're being asked is