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Relative velocity question

  1. Dec 5, 2012 #1
    1.Two particles A and B have velocities 3i and vj respectively (in m/s).



    (a) Find the position of B relative to A for all t given that r (b relative to a)
    (t=0) = -9i+6j (in metres).

    (b) Find the value of v such that A and B collide.

    (c) If v=1 m/s, find the time and distance when A and B are closest together.



    3. Well, firstly i drew it out. A= 3i+0j , B=0i+vj. Then I integrated A and B and let it equal to -9i+6j and I got t=3 and v=2. I also got the angle to be 33.69°. I don't know what to do after that of if anything i got is right.
     
    Last edited: Dec 5, 2012
  2. jcsd
  3. Dec 5, 2012 #2
    Is that the way the problem statement is stated your textbook?

    If particle [itex] A [/itex] is only moving along the [itex] x-axis [/itex] and particle [itex] B [/itex] is only moving along the [itex] y-axis [/itex], their relative position is always going to be the hypotenuse of a right triangle with a side being a multiple of [itex] 3 [/itex] and another being a multiple of [itex] v [/itex]. Can you figure out what the expression for the position of [itex] B [/itex] relative to [itex] A [/itex] for all [itex] t [/itex] is given their relative position at [itex] t=0 [/itex]?
     
  4. Dec 5, 2012 #3
    Yes, that is the way the problem is stated.

    So the relative position is vj-3i ?
     
  5. Dec 5, 2012 #4

    haruspex

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    No, that's the relative velocity. You were right to integrate that (I assume v is constant).
    But I'm not sure what you meant by this:
    I integrated A and B and let it equal to -9i+6j and I got t=3
    When you integrate you get an unknown constant, and you have to find the value of that from initial conditions. What general formula did you get for relative position?
     
  6. Dec 6, 2012 #5
    When I integrate A= 3i , I will get 3ti + constant and B= vj so that it will be vtj + constant. I added the t because, the answer has to be with respect to time. And then I let it equal to -9i+6j= -3ti +vtj

    So you mean that relative position is basically + vtj -3ti because its B relative to A.

    And from that I can say that v has to be 2 for them to collide, but what about part 3?
     
    Last edited: Dec 6, 2012
  7. Dec 6, 2012 #6

    haruspex

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    Right so far.
    No. You need to find out what the two constants are. To do that you use the information about the position when t = 0.
     
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