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Math Help - Earth Rotation Speed Q

  1. #1
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    Earth Rotation Speed Q

    I wasn't sure which exact board to post this in, so I thought I'd start with this one

    A friend and I were discussing the speed in which the earth spins at the equator. I had to look it up, in which it's speed is 1,038 Miles Per Hour. So this brought on the question of flying from East to West and from West to East and how much ground would be covered in one hour.
    So the question is:

    Using the above data, if you were in a jet plane traveling at 1,000 Miles Per Hour flying from East to West, how many miles are covered in one hour?

    Alternately, if traveling in a jet plane at 1000 Miles Per Hour from West to East, how long would it take to cover the same amount of miles in the first question? Time in hours, mins, and seconds.

    This is probably easy for most everyone here, and I came up with an answer, but I'm not sure if I'm right or not. I came up with 2,038 for the first question, and 2 hours 2 mins and 30 seconds for the second. But I don't know if I'm right! lol

    TIA
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  2. #2
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    Hello, Ineedhelp314!

    A friend and I were discussing the speed in which the Earth spins at the Equator.
    I had to look it up, in which its speed is 1,038 mph.
    So this brought on the question of flying from East to West and from West to East
    and how much ground would be covered in one hour.

    So the question is:
    Using the above data, if you were in a jet plane flyijng East to West at 1,000 mph,
    how many miles are covered in one hour?
    . . Measured from where?
    Are we assuming that an object somwhere above the Equator
    . . is not carried carried around the planet?


    At time-zero, the jet is directly above point A on the Equator.

    In one hour point A has moved 1038 miles to the east.
    In the same hour, the jet has flown 1000 miles to the west.

    The jet is now 2038 miles west of point A.




    Alternately, if flying West to East at 1000 mph,
    how long would it take to cover the same distance?

    Point A on the Equator is moving east at 1038 mph.
    The jet is flying east at only 1000 mph.
    . . The jet will never overtake point A.

    However, the question is:
    . . How long does it take for the jet to fly 2038 miles?


    Answer: . \frac{\text{2038 miles}}{\text{1000 mph}} \;=\;2.038\text{ hours} \;=\;\text{2 hours, 2 minutes, 16.8 seconds}


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    **

    Consider standing on the Equator and throwing a ball straight upward
    . . so that it falls into your hand one second later.
    This is quite normal and expected.

    With your scenario, while the ball is in the air for one second,
    . . the Earth has moved 1548.8 feet to the east.
    It will come down over a quarter-mile to the west of you.

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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Soroban View Post

    **

    Consider standing on the Equator and throwing a ball straight upward
    . . so that it falls into your hand one second later.
    This is quite normal and expected.

    With your scenario, while the ball is in the air for one second,
    . . the Earth has moved 1548.8 feet to the east.
    It will come down over a quarter-mile to the west of you.
    This is essentially Galileo's thought experiment in "Dialogue Concerning the Two Chief World Systems" of dropping a weight from the mast head of a moving ship (which is not exactly Galileo's experiment but is a variant of it).

    I always thought that on a moving ship the distance moved by the ship in the time it takes a weight to fall would be negligable but was moved to make the calculation after seeing the film "Agora" in which Hypatia of Alexandria is shown having this experimant performed.

    The result is, assuming that the ship is moving at 2m/s (or ~4kts) and a mast height os 10m the distance is ~3m which is quite substantial (the experiment of jumping or throwing things that Galileo advocates, would have a significantly less observable effect on a ship moving at such a speed, which is why dropping the weight from tha mast head is better in this respect though more influenced by the ships other motions).

    Note you need to assume that the ships roll pitch and heave have negligable effect on where the weight falls.

    CB
    Last edited by CaptainBlack; June 3rd 2010 at 11:21 PM.
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  4. #4
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    That is awesome! Thanks guys for your quick responses! And to Soroban, your response actually raised more questions to my continuously curious mind lol. I understand why the ball in this scenario wouldn't land 1/4 mile away in real life, I'm assuming because since we are all traveling (well, if we we're at the equator) at 1,038 mph, including the ball if I threw it up in the air, kinda like throwing something out of a car window when going 60mph down the highway, it keeps up until eventually losing speed by encountering wind resistance, but in real life, the wind is traveling the same speed as the earth rotation, on a calm day that is. SO with that said, in your response you stated that the plane traveling West to East would never catch up to point A if it maintained the 1000mph speed. So how exactly do planes fly from West to East when the top speed is only 500-600mph? I tried to look this up, but found nothing except that it was stated that most planes will use the Jet Stream when possible to save fuel, which speed is about the same.
    I mean, I'm no expert in aeronautics by any means obviously, but for some reason, I can't figure this one out either lol.
    Oh well, I know that's probably not a math related question, but thanks for answering my original question
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  5. #5
    Senior Member Mukilab's Avatar
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    I am also confused. Surely they would have to travel even faster because they are in the air?

    The only explanation of this from the basic physics knowledge I have is that there is some form of centrifugal force in action.
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