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Homework Help: What is the speed of each particle relative to the other?

  1. Nov 2, 2006 #1
    Two particles are shot out simultaneously from a given point with velocity v. They start at right angles to each other. What is the speed of each particle relative to the other?

    I got one particle thinks the other one is travelling at [tex]v\sqrt2[/tex] whereas they are travelling at v and vice versa. But I think I calculated it from a frame that is at rest relative to both particles and imagined what each particle would think if they had information in my frame.
    Last edited: Nov 2, 2006
  2. jcsd
  3. Nov 2, 2006 #2

    Andrew Mason

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    If you stick to a vector analysis, it is not so confusing. The relative velocity of a to b is the velocity of a relative to the origin - velocity of b relative to the origin (or + the velocity of the origin relative to b). So just subtract the velocity vectors.

    The relative velocity, therefore is [itex]\vec v_a + (-\vec v_b)[/itex]. Relative speed is the length of that vector, which is the hypotenuse of a right triangle with sides of length v: [itex]v_{rel}\sqrt{2v^2} = \sqrt{2}v[/itex].

    Last edited: Nov 2, 2006
  4. Nov 2, 2006 #3
    So veclocity of a to b is usually just [itex]\vec v_a -\vec v_b[/itex].

    So if we look at another example, ship a is travelling at 4c/5. ship b is travelling at 3c/5 in 1D motion. The relative velocity of ship a to b or what ship b thinks a is travelling is [itex]v_a -v_b = c/5[/itex].
    Last edited: Nov 2, 2006
  5. Nov 2, 2006 #4


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    If the speeds are relativistic and in different directions, you need to use the vector form of the relativistic "velocity addition" formula. See the section "The velocity addition formula for non-parallel velocities" on the following page from the Usenet Physics FAQ:

    Last edited: Nov 2, 2006
  6. Nov 3, 2006 #5
    But if I am just doing velocity addition for different frames (not events in frame), i.e know what the other frame is travelling relative to me, do I still need the relativistic addition formula? If I do apply it than I could pretend the 'event' is a person standing still in the other frame. So the velocity of that person is 0 in their frame S'. I get the speed I see them is v the relative velocity of the frames. This value can be calculated with the method I suggested in #3?
  7. Nov 3, 2006 #6

    Doc Al

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    Staff: Mentor

    Yes. The relativistic addition formula tells you how velocities transform from one frame to another, which is what you want.
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