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Homework Help: Finding the average speed

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Any person on the Earth is carried in a cirular path as the Earth rotates on axis. The Earth revolves once in a day. At a latitude of Φ, the distance to the axis of rotation is R = REarthcos(Φ). If Anytown's latitude is 48.8 degrees and the Earth's radius is 6378 km, what is your average speed at Anytown's latitude due to the Earth's rotation? Express your answer in m/s.


    2. Relevant equations
    R = REarthcos(Φ)
    velocity=distance/time


    3. The attempt at a solution
    I tried first to switch the earth's radius from kilometers into meters to get it into the right format of m/s. I tried then to put it into the equation for the distance to the axis of rotation...R=(6378000)*cos(48.8) and then divide that number by the number of seconds in a day (86400) but I don't get the right answer. I think I'm just confusing myself more than anything else. Any help would be appreciated!
     
  2. jcsd
  3. Sep 28, 2010 #2

    jhae2.718

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    [tex]R_E\cos(\phi)[/tex] is not the total distance traveled. It is just the distance to the axis of rotation. You need to come up with an expression for the total distance traveled in a day at that latitude.
     
  4. Sep 28, 2010 #3
    Oh I see. I guess I just don't understand how to come up with an expression with the information provided or how to use the equation given properly.
     
  5. Sep 28, 2010 #4

    jhae2.718

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    If you have a radius, and assume the Earth is circular in cross section, what is the distance around it? Think geometry.
     
  6. Sep 29, 2010 #5
    Ok. So then I need to find the circumference to find the total distance traveled?

    C=pi*r2
    C=pi*(6378)2= 127796483.1
     
  7. Sep 29, 2010 #6

    jhae2.718

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    The circumference is [tex]C=2\pi r[/tex]. What you have is area.
     
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