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Relative motion

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Car A is travelling west at 60 km/hr.
    Car B is travelling north at 70 km/hr.
    The cars intersect at point O.
    When Car A is x km east of and Car B is y km south of O, the distance between the cars is z km.
    Find the rate of change of z when x = .8 km and y = .6 km.

    3. The attempt at a solution

    In my physics class, we would do this problem with anti-derivatives with initial conditions.
    However, in my calc class, we haven't learned this yet.

    VA = (-60 km/hr) i

    VB = (-70 km/hr) j


    So,

    rA = (-60t + x) i

    rB = (-70t + y) j


    z = rB + rB = (-60t + x) i + (-70t + y) j

    From here, do I take the derivative of z to get dz/dt?

    Also, if someone could tell me how to start this problem without using anti-derivatives, that would be great.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 18, 2009 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    You are given dx/dt, dy/dt and know z2 = x2 + y2, where all the variables are functions of t.

    Differentiate this equation implicitly with respect to t and plug your numbers in.
     
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