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Math Help - How Far Can a Pilot See?

  1. #1
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    How Far Can a Pilot See?

    On a recent flight to San Francisco, the pilot announced that we were 139 miles from the city, flying at an altitude of 35,000 feet. The pilot claimed that he could see the Golden Gate bridge and beyond. Was he telling the truth? How far could he see?
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  2. #2
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    Any hint given about what is supposed to be limiting the distance he can see? If nothing else is in the way, I would guess that it's determined by the curvature of the earth. Does that help? Try drawing a diagram of the situation and figure out what is the furthest point he can see. [I calculated it based on this and I got a distance of 229 miles at 35000 feet]
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  3. #3
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    tell me...

    Read my reply through yours:

    Any hint given about what is supposed to be limiting the distance he can see?[No, hints leading to the right answer].

    If nothing else is in the way, I would guess that it's determined by the curvature of the earth. Does that help?[What do you mean by curvature of the earth]?

    Try drawing a diagram of the situation and figure out what is the furthest point he can see. [I calculated it based on this and I got a distance of 229 miles at 35,000 feet]

    Can you further explain your reasoning?

    Can you provide steps?
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  4. #4
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    Quote Originally Posted by blueridge View Post
    Read my reply through yours:

    Any hint given about what is supposed to be limiting the distance he can see?[No, hints leading to the right answer].

    If nothing else is in the way, I would guess that it's determined by the curvature of the earth. Does that help?[What do you mean by curvature of the earth]?

    Try drawing a diagram of the situation and figure out what is the furthest point he can see. [I calculated it based on this and I got a distance of 229 miles at 35,000 feet]

    Can you further explain your reasoning?

    Can you provide steps?
    You need a diagram:


    In the diagram d is the distance to the horizon from a height h

    Now use that radius of the Earth in milles for R, convert 35000ft to miles and use that for h.

    Now you need to calculate d (in miles). Is this more or less than the distance
    to the Golden Gate?

    RonL
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  5. #5
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    Ron

    Ron,

    Are you saying that from your diagram I can set up this equation?

    d^2 + R^2 = (h + R)^2

    All I have to do now is plug the numbers and simplify.

    Is this correct?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by blueridge View Post
    Ron,

    Are you saying that from your diagram I can set up this equation?

    d^2 + R^2 = (h + R)^2

    All I have to do now is plug the numbers and simplify.

    Is this correct?
    Yes

    (there is a slight complication if you have to allow for the height of the
    bridge, but I don't thing that is a problem here)

    RonL
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