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Help with vector exam questions (M1)

  1. Aug 31, 2007 #1
    Hi.

    I have no idea how to even begin to do this question and so I would really appreciate any help.

    Two helicopters P and Q are moving in the same horizontal plane. They are modelled as particles moving in straight lines with constant speeds. At noon P is at the point with position vector (20i + 35j) km with respect to a fixed origin O. At time t hours after noon the position vector of P is p km. When t = 0.5 the position vector of P is (50i - 25j) km. Find

    (a) the velocity of P in the form (ai + bj) km/h,

    I got this as (60i - 120j) km/h.

    (b) an expression for p in terms of t.

    Thank you.

    Cathy
     
  2. jcsd
  3. Aug 31, 2007 #2

    Doc Al

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    How does distance relate to velocity and time?

    (This seems better suited for Intro Physics than Calc & Beyond--I'll move it.)
     
    Last edited: Aug 31, 2007
  4. Aug 31, 2007 #3
    Ok, thanks.

    Would I use v = s/t?

    Cathy
     
  5. Aug 31, 2007 #4
    You should start with the basic equations of kinematics and go on from there.
     
  6. Aug 31, 2007 #5

    learningphysics

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    Yes, but here s = final position - initial position...

    or you can just use sfinal = sinitial + vt
     
  7. Aug 31, 2007 #6

    Doc Al

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    Yes.

    You have the initial position vector. You know how each component changes with time, so you can find the position vector at any time t.
     
  8. Aug 31, 2007 #7
    Thanks everyone for your help.

    Sorry, but I still don't see how I can get an expression for p in terms of t.

    Cathy
     
  9. Aug 31, 2007 #8

    learningphysics

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    p is just the final position in the equation (the final position of helicopter P after t amount of time passes):

    v = (final position - initial position)/t

    solve for final position... then you can plug in initial position and velocity since you know those already...
     
  10. Aug 31, 2007 #9
    Okay - thanks so much for your help!

    I got p = (60t + 20)i + (35 - 120t)j km.

    Cathy
     
  11. Aug 31, 2007 #10

    learningphysics

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    looks good!
     
  12. Aug 31, 2007 #11
    Thank you.

    I'm not sure now how to do this next part. Could you please help again?

    At noon Q is at O and at time t hours after noon the position vector of Q is q km. The velcoity of Q has magnitude 120 km/h in the direction 4i - 3j. Find

    an expression for q in terms of t.


    Thanks so much!

    Cathy
     
  13. Aug 31, 2007 #12

    learningphysics

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    Try to get the velocity of Q as a vector... Use the magnitude of the velocity which is given... along with a unit vector in the given direction...

    So the first step is to get the unit vector in the given direction.
     
  14. Aug 31, 2007 #13
    Would I use Pythagoras?

    Cathy
     
  15. Aug 31, 2007 #14

    learningphysics

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    Yes... have you studied unit vectors in your class? You divide the vector by its magnitude...
     
  16. Aug 31, 2007 #15
    I'm really not sure what to do.

    Could you please show me the steps?

    Thank you.

    Cathy
     
  17. Aug 31, 2007 #16

    learningphysics

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    First step is to find the unit vector in the direction of 4i-3j... so first find the magnitude of this... it is [tex]\sqrt{4^2 + (-3)^2} = 5[/tex]

    So then the unit vector in the direction of 4i - 3j is [tex]\frac{1}{5}(4i-3j) = \frac{4}{5}i - \frac{3}{5}j[/tex]

    Multiply this vector by 120km/h... and that's your velocity vector. So the velocity of Q is:

    [tex]120(\frac{4}{5}i - \frac{3}{5}j) = (96i -72j) km/h[/tex]

    Now you can use this velocity to find q... using the fact that the initial position = 0i + 0j... so now it is just like the previous problem...

    In general when you need a vector of a particular magnitude in a particular direction... you multiply the magnitude by a unit vector in that particular direction...

    Hope this helps...
     
  18. Aug 31, 2007 #17
    Thank you so much for your help!

    Cathy
     
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