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Relative velocity

  1. May 14, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle , P moves on a horizontal plane along the circumference of a circle with centre O and a radius of 3m at an angular velocity of pi/4 rad/s in the clockwise direction . A second particle , Q moves on the same plane along a circle with radius 2m and the same centre as the first circle at an angular velocity of pi/2 rad/s in the clockwise direction . At first , O, P and Q are collinear with P and Q located at the north of O . Find the magnitude and direction of the velocity of P relative to Q .

    2. Relevant equations



    3. The attempt at a solution

    the angular displacement of P and Q are 3pi/4 and 3pi/2 respectively .

    The linear velocities of P and Q are 3pi/4 and pi respectively .

    then one of the angle of the triangle is 3pi/4

    so i can use the cosine rule ,

    |pVq|^2=pi^2+(3pi/4)^2-2pi(3pi/4)cos (3pi/4)

    |pVq|=5.49 m/s

    bu the answer given is 5.09 m/s

    where did i go wrong ?
     

    Attached Files:

  2. jcsd
  3. May 14, 2010 #2

    tiny-tim

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    Hi thereddevils! :smile:

    (have a pi: π and try using the X2 tag just above the Reply box :wink:)
    (i assume this is to be calculated after 3 seconds?)

    General tip: take out any awkward factors first … then you're less likely to make mistakes, and if you do make one, you're more likely to see where it is.

    Then your equation is (π/4)2 times (9 + 16 + 2*3*4*1/√2) = (π/4)2(25 + 12√2) … :wink:
     
  4. May 14, 2010 #3
    thanks tiny , is my mistake in the calculation in the cosine rule , or the diagram is wrong ?
     
  5. May 14, 2010 #4

    tiny-tim

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    I think your calculator is wrong. :redface:
     
  6. May 14, 2010 #5
    lol !!!!!! , its in radians mode :grumpy:

    thanks a lot !!
     
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