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Math Help - [SOLVED] calculating the length of a shadow

  1. #1
    romed
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    [SOLVED] calculating the length of a shadow

    How does one calculate the lenth of a shadow at any given time
    lets say my latitute is 36 degrees.

    And the height of the object is 1.2 meteres

    also how do i claculate when the length of the shadow is the same as the height thats is 1.2 meters

    Thanks Rod
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  2. #2
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    A real calculation of the length of shadow is non-trivial and is in the domain of celestial navigation. See here for calculators for educational purposes.
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  3. #3
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    Quote Originally Posted by romed
    How does one calculate the lenth of a shadow at any given time
    lets say my latitute is 36 degrees.
    And the height of the object is 1.2 meteres
    also how do i claculate when the length of the shadow is the same as the height thats is 1.2 meters
    Thanks Rod
    Hello,

    I can give you only a few informations:

    1. When the sun is perpendicular over the tropic it has it's maximum altitude over the horizon at 12 o'clock local time . At a latitude of 36N the maximum altitude of the sun is approximately 77.5 over the horizon. Then you get the shortest shadow:
    s=1.2 m \cdot \cot(77.5^\circ) \approx 26.6 cm

    The longest shadow you get when the sun touches the horizon: The shadow has an infinite length.

    2. When the shadow is as long as the stick itself, then the sun has a altitude of 45 over the horizon. This situation will happen twice a day in the summer.
    In winter the maximum altitude of the sun reaches only approximately 30.5 (at 36N, of course!). That means the shortest shadow will have a length of

    s=1.2 m \cdot \cot(30.5^\circ) \approx 2.04 m

    I hope these informations are of some use to you.

    Greetings

    EB
    Last edited by earboth; May 11th 2006 at 06:32 AM.
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  4. #4
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    Quote Originally Posted by romed
    How does one calculate the lenth of a shadow at any given time
    lets say my latitute is 36 degrees....

    Thanks Rod
    Hello,

    it's me again.

    I've attached a diagram, to demonstrate where all my numbers came from.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails [SOLVED] calculating the length of a shadow-shadow.gif  
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  5. #5
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    Quote Originally Posted by earboth
    Hello,

    I can give you only a few informations:

    1. When the sun is perpendicular over the tropic it has it's maximum altitude over the horizon at 12 o'clock local time . At a latitude of 36N the maximum altitude of the sun is approximately 81 over the horizon. Then you get the shortest shadow:
    s=1.2 m \cdot \cot(81^\circ) \approx 19 cm

    The longest shadow you get when the sun touches the horizon: The shadow has an infinite length.

    2. When the shadow is as long as the stick itself, then the sun has a altitude of 45 over the horizon. This situation will happen twice a day in the summer.
    In winter the maximum altitude of the sun reaches only approximately 27 (at 36N, of course!). That means the shortest shadow will have a length of

    s=1.2 m \cdot \cot(27^\circ) \approx 2.36 m

    I hope these informations are of some use to you.

    Greetings

    EB
    Hi. According to this page from NASA, the maximum and minimum altitudes of the sun at latitude L are given by 90 - L \pm 23.5, which for L = 36 yields 77.5 and 30.5. How did you calculate your maximum and minimum?
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  6. #6
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    Quote Originally Posted by JakeD
    Hi. According to this page from NASA, the maximum and minimum altitudes of the sun at latitude L are given by 90 - L \pm 23.5, which for L = 36 yields 77.5 and 30.5. How did you calculate your maximum and minimum?
    Hello,

    you are right. Instead of 23.5 I took 27. I can only guess why I use this number: The polar circle has a latitude of nearly 67 (and I'm living nearer to the polar circle than to the 36N regions) and so I mixed up those ciphers. So sorry!

    Greetings

    EB
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