Relative motion/velocity help

  • Thread starter fsm
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  • #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.
 

Answers and Replies

  • #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.
 
  • #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?
 
  • #4
radou
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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?

How did you get that result? According to my calculations, this is wrong.
 
  • #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
 
  • #6
radou
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7*cos(75)i+7*sin(75)j=5.5i+0j+[tex]\vec{v}_{M,B}[/tex]

Your calculation is wrong - the line above implies
[tex]\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}[/tex].
 
  • #7
fsm
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ok I think I found my error. Now I get 7.7 m/s @ 119 degrees.
 
  • #8
fsm
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Well I guess that one is wrong too. I don't see what I'm doing wrong.
 
  • #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.
 
  • #10
fsm
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Could anyone verify this?
 
  • #11
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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
 
  • #12
fsm
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Now when I did that radou said it was wrong. I have no idea now.
 
  • #13
radou
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Now when I did that radou said it was wrong. I have no idea now.

You didn't do that. You set the equation up correctly, and then miscalculated. EthanB is right, too.
 
  • #14
fsm
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I still get -3.68i
 
  • #15
fsm
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Please could someone tell me what I'm doing wrong? I don't get it.
 
Last edited:
  • #16
fsm
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I'm not trying to be a pest, but anyone?
 
  • #17
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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].

I still get -3.68i

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].
 
  • #18
fsm
88
0
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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