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Relative velocity of two speeding cars

  1. Mar 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Given the following conditions, what is the relative velocity of 2 cars if their ground speeds are 80km/h for Car A and 45 km/h for Car B?
    a) both cars are heading in the same direction, A behind B in the reference frame of A
    b) Use the reference frame of B for part A)
    c) both cars are heading towards each other. take the reference frame of A
    d) use B's reference frame for part c.

    2. Relevant equations
    none. i just used simple addition + subtraction.

    3. The attempt at a solution
    basically the wording of this problem is really throwing me off. i dont understand what they're trying to ask me to do evne though it seems like an easy question.

    im guessing that 35km/h will be the answer for A and B? because i figured if you were sitting in car B, it seems like car A is just going 35 km/h faster..?
    please help. thanks
  2. jcsd
  3. Mar 2, 2008 #2
    The related information from Physics.
    Velocity definition: Velocity is speed in a known direction.
    Relative Velocity definition: The velocity of an object, A, relative to any other choosen object, B, having velocity, including stationary objects.

    General calculation:
    Let the velocity of object, A be equated to v1, while the velocity of object, B is equatable to v2. The relative velocity of A with respect to B is written as, Rv(v1,v2), WHEREAS, the relative velocity of B with respect to A is written as, Rv(v2,v1), which is short for Rv(+v1,+v2).

    The calculation, Rv(v1,v2) is, Rv(v1,v2) = v1-v2 = (+v1) - (+v2) ;
    The resulting value can be positive (+), negative (-), or zero (0).

    Because velocity is speed in a known direction, solving physics problems of this nature,
    means assigning the directions of travel, in a sane, comprehensive manner. The normal
    assignments for direction, starts within the frame of reference, which has been agreed
    upon, as positive. Therefore Rv(v1,v2), at least means, that v1 is aligned with a positive
    direction. This implies that assignments for direction are done in sequential order, and the
    frame of reference is given itz direction, first, before all others.

    Any object B, with velocity v2, moving in the same direction, as the direction, the frame
    of reference indicates, yields a direction, identical to the frame of reference, (positive)
    and the relation written Rv(+v1,+v2) which is identical to Rv(v1,v2).

    Any object B, moving in the opposite direction as the direction the frame of reference
    indicates, itz directional relationship to the frame of reference is, the opposite,
    (negative) and the relation written Rv(+v1,-v2), which is the same as Rv(v1,-v2).

    Velocity is a vector (directional) whereas speed is a scalar (non directional).
    Here are the steps:
    (1) From the given information construct your frame of reference (v1).
    (2) Write down the equivalence relation of Rv(v1,v2)
    (3) Calculate the relative velocity Rv(v1,v2) = (v1) - (v2), keeping the sign.
    (4) Write your answer clearly, with direction and appropriate units.

    Shall we proceed?

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