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Homework Help: Relative motion/velocity help

  1. Nov 25, 2006 #1

    fsm

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    I need some help with this question:

    Two cars, a Volkswagen Beetle travels east @ 5.5 m/s and a Ford Mustang traveling @ 75 degrees north of east @ 7 m/s. Both cars start from the same position and t=0.

    a. What is the velocity of the Mustang with respect to the Beetle?
    b. What is t when both are 60 m away from each other?
    c. What is d after t=5 sec?


    I am having a tough time with relative motion. I've read that section a million times. I can solve it by just treating it as a simple vector problem, but the teacher wants using the formula v=v' + V0. So for a do I resolve each vector into its i and j components and add? I'm really confused.
     
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  3. Nov 25, 2006 #2

    radou

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    [tex]\vec{v}_{M} = \vec{v}_{B} + \vec{v}_{M,B}[/tex], where M stands for Mustang, B for Beetle, and M, B for Mustang relative to Beetle. You know the velocity vectors, since the magnitudes and directions are given. Try to start with that.
     
  4. Nov 25, 2006 #3

    fsm

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    [tex]\vec{v}_{M,B}[/tex]=8.12 m/s @ 124 degrees

    Is it now just a kinematics problem for b and c?
     
  5. Nov 26, 2006 #4

    radou

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    How did you get that result? According to my calculations, this is wrong.
     
  6. Nov 26, 2006 #5

    fsm

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    7*cos(75)i+7*sin(75)j=5.5i+0j+[tex]\vec{v}_{M,B}[/tex]

    -4.49i+6.76j=[tex]\vec{v}_{M,B}[/tex]

    R=sqrt((-4.49)^2+(6.76)^2)
    R=8.12 m/s

    theta=arctan(6.76/-4.49)
    theta=-56.4 degrees
    theta=180-56.4
    theta=124 degrees
     
  7. Nov 26, 2006 #6

    radou

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    Your calculation is wrong - the line above implies
    [tex]\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}[/tex].
     
  8. Nov 26, 2006 #7

    fsm

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    ok I think I found my error. Now I get 7.7 m/s @ 119 degrees.
     
  9. Nov 26, 2006 #8

    fsm

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    Well I guess that one is wrong too. I don't see what I'm doing wrong.
     
  10. Nov 26, 2006 #9

    fsm

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    [tex]\vec{v}_{M,B}=7.31\vec{i}+6.761\vec{j}[/tex] is what I get now.
     
  11. Nov 26, 2006 #10

    fsm

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    Could anyone verify this?
     
  12. Nov 27, 2006 #11
    You got 7.31 by adding the i hats, rather than subtracting. It should be (sorry, no LaTeX)

    (7*cos(75)-5.5)i+(7*sin(75))j=Vrelative
     
  13. Nov 27, 2006 #12

    fsm

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    Now when I did that radou said it was wrong. I have no idea now.
     
  14. Nov 27, 2006 #13

    radou

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    You didn't do that. You set the equation up correctly, and then miscalculated. EthanB is right, too.
     
  15. Nov 27, 2006 #14

    fsm

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    I still get -3.68i
     
  16. Nov 27, 2006 #15

    fsm

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    Please could someone tell me what I'm doing wrong? I don't get it.
     
    Last edited: Nov 27, 2006
  17. Nov 27, 2006 #16

    fsm

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    I'm not trying to be a pest, but anyone?
     
  18. Nov 27, 2006 #17
    That's exactly what you should be getting. I think you misread what radou said: he said that the numbers you got were wrong, that you should've (from your data) gotten [tex]\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}[/tex].
     
  19. Nov 27, 2006 #18

    fsm

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    I get it now. I just have been working on this problem so much. Thank you both radou and EthanB for your help.
     
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