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Circular movement

  1. Sep 4, 2005 #1
    hi ,
    I have a problem about vector coordinates. this is the problem.

    We have a 2-dimension space [x(unit vector i) and y( unit vector j)].

    I have a circle of center 0 (0,0) and a point P such that OP = r.

    Vector OP and the x-axis have an angle of θ .

    there is a unit vector ir , with the same direction with OP( but starting at P.)

    Another unit vector it starts at P , but it is perpendicular to vector ir. ( it 's direction is toward north-west)

    Express vector ir as a combination of unit vectors i and j.

    Express vector it as a combination of unit vectors i and j.

    I found that ir = cos(θ ) i + sin(θ ) j

    how to find it ? when I try to compute for it, I found the same as ir, but I am not sure.

    Please help

    Thank you
  2. jcsd
  3. Sep 4, 2005 #2

    Doc Al

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    Staff: Mentor

    Since it is perpendicular to ir, they cannot have the same components. Draw a careful diagram. (I suspect you are mixing up your sines and cosines.)
  4. Sep 4, 2005 #3
    OK, I follow your suggestion and now I find:

    it= sin(θ )i +cos(θ ) j

    I do not know if you did the problem but I believe it is ok now
  5. Sep 4, 2005 #4

    Doc Al

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    Staff: Mentor

    It's almost right. To see what's wrong, test if these vectors are perpendicular.
  6. Sep 5, 2005 #5
    Doc please I need help for this problem. Someone reply me but I need more information to complete it. It is urgent !

    This is a problem I have . But because I cannot include the graph, I try to do via Microsoft Word. I put it as an attachment. I hope that you will understand it.

    This is the problem:

    Traffic signals are placed along a straight road at positions x = 0 m, x = 600 m, and x = 1200 m (see graph in attachment)). The time intervals during which the signals are green are shown by the thick lines ( in red) in the figure.

    (a) Draw the displacement-versus-time curves (fastest and slowest) for a car that passes through all the lights when the car moves with constant speed.

    (b) Draw a similar set of lines for a car traveling in the opposite direction.

    (c) Assuming that the lights are timed such that a car passes through all lights in the middle of the time interval, what is the speed for which the lights are timed?

    (d) What is the fastest constant speed of a car that makes it through all the signals, assuming it arrives at the first light at the optimal moment?

    For info.:
    The grah is a 2 dimension space with time(s) on horizontal and the position x(m) in vertical.
    The interval are put in red and I mentioned the time interval at the end of each line.Please help me with that . I do not understand it

    Thank you very much.


    Attached Files:

  7. Sep 5, 2005 #6


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    Staff Emeritus
    Science Advisor

    Did you read Doc Al's last post:
    "It's almost right. To see what's wrong, test if these vectors are perpendicular."

    You had said " ir = cos(θ ) i + sin(θ ) j" and "it= sin(θ)i+ cos(θ)j"

    Remember that the dot product of two perpendicular vectors is 0. Here the dot product would be cos(θ)sin(θ)+sin(θ)cos(θ).
    Do you see what is wrong? Now look at your picture again.
  8. Sep 5, 2005 #7
    I got it
    it =-sin(θ)i+ cos(θ)j

    Please can take a look at the problem ( about the car and the 3 lights) just above this quote. I do not know if Doc will be available today.

    Please give some suggestions.

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