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# A.S. Question 18 Gateway Arch

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### A.S. Question 18 Gateway Arch - Page Text Content

BC: S U M M A R Y

FC: Gateway Arch | Angelina Smith

1: On a trip to Saint Louis you visit the Gateway Arch. Since you have plenty of time on your hands, you decide to estimate its altitude. You know that the arch is 162 meters wide at the base. To find another point on the arch, you measure a value of y=4.55 meters when x=1 meter. Assume that the arch is parabolic. * In order to find out the equation of the parabola that represents the underside of the arch you need three points. What are they, given the information above? * Find the equation of the underside of the arch. * What is the height of the arch? *An airplane with a wingspan of 40 meters tries to fly through the arch at an altitude of 170 meters. Could the plane possibly make it? Justify your answer. *At what altitude would the plane's wingspan be too wide to fly under the arch?

2: In order to find out the equation of the parabola that represents the underside of the arch you need three points. What are they, given the information above? | The points that can be gathered from the given information above are: * (0, 0) * (1, 4.55) * (162, 0)

3: Find the equation of the underside of the arch.

4: What is the height of the arch? | Using the maximum key on a graphing calculator, you can easily calculate the precise height of the arch. When used the height comes out to 185.4 meters tall.

5: An airplane with a wingspan of 40 meters tries to fly through the arch at an altitude of 170 meters. Could the plane possibly make it? Justify your answer.

6: An airplane with a wingspan of 40 meters tries to fly through the arch at an altitude of 170 meters. Could the plane possibly make it? Justify your answer. | Yes the plane could make it through the arch at an altitude of 170 meters. This is true because the points on the arch at this altitude subtract to equal 46.8 meters. The plane's wing span is only 40 meters therefore making it possible to for the plane to fly underneath the Gateway Arch with 6.8 meters left to spare

7: At what altitude would the plane's wingspan be too wide to fly under the arch? | At an altitude of 180 meters, it would be impossible for the plane to fly underneath the arch. This is because of the corresponding points on the parabola are 94.8 and 67.1. To find the length across the parabola between those two points, you simply subtract the two points. When this is done the product you obtain is 27.7 meters. The wing span of the airplane is 40 meters therefore making it impossible for the airplane to fly under the arch at this altitude. .

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