1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Relative motion/velocity help

  1. Nov 25, 2006 #1

    fsm

    User Avatar

    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.
     
  2. jcsd
  3. Nov 25, 2006 #2

    radou

    User Avatar
    Homework Helper

    [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

    User Avatar

    [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

    User Avatar
    Homework Helper

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

    fsm

    User Avatar

    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

    User Avatar
    Homework Helper

    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

    User Avatar

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

    fsm

    User Avatar

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

    fsm

    User Avatar

    [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

    User Avatar

    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

    User Avatar

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

    radou

    User Avatar
    Homework Helper

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

    fsm

    User Avatar

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

    fsm

    User Avatar

    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

    User Avatar

    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

    User Avatar

    I get it now. I just have been working on this problem so much. Thank you both radou and EthanB for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?