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Math Help - What's the max height a 747 plane can fly, under the St.louis arch?

  1. #1
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    Cool What's the max height a 747 plane can fly, under the St.louis arch?

    I'm trying to figure out how to estimate the max height a Boeing 747 can fly, if it were to fly under/through the St.Louis gateway arch?

    The equation for the arch is y = 693.8597 - 68.7672 cosh ( 0.0100333 x )

    Wingspan 195 ft 8 in (59.6 m)
    Tail height 63 ft 5 in (19.3 m)


    And the Arch is 630ft tall and 630ft wide at the base.

    Also, i'd like to also figure our other wingspans also. What would be the way to sovle this?
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  2. #2
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    Hello, StuG1944!

    I'm trying to figure out how to estimate the max height a Boeing 747 can fly,
    if it were to fly under/through the St.Louis gateway arch?

    The equation for the arch is: . y \:=\:693.8597 - 68.7672\cosh( 0.0100333x)

    Wingspan: .195 ft 8 in
    Tail height: . 63 ft 5 in

    And the Arch is 630 ft tall and 630 ft wide at the base. . really?


    Also, i'd like to also figure our other wingspans also.
    What would be the way to sovle this?

    The wingspan is: . 195\frac{2}{3} \:=\:\frac{587}{3}\text{ ft.}

    Then: . x \;=\;\frac{587}{6}

    Hence: . y \;=\;693.8597 - 68.7672\cosh[0.0100333(\frac{587}{6})]

    . . . . . . y \;=\;589.2161828


    To clear the wingspan of the Boeing, it can fly as high as 589.2 feet.

    But this leaves only 630 - 589.2 \:=\:41.8 feet clearance at the top.
    And this does not allow for the height of the tail, 63\frac{5}{6} feet.


    Therefore, the maximum altitude of the Boeing is:
    . . 630 - 63\frac{5}{12} \;=\;566\frac{7}{12} feet.

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  3. #3
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    Thanks for the help! Just sent a donation to the forum for it.
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