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Radar problem

  1. Jul 17, 2014 #1
    1. The problem statement, all variables and given/known data
    You are standing on side of road and ambulance drives by. Smallest distance between you and ambulance is 4m. Ambulance v=10m/s^2. You have 2.2 GHz radar. Ambulance travels 100m with center of straight line directly across from you.
    Compute exact doppler shift by taking derivative of range vs time equation.
    Give ambulance acceleration


    2. Relevant equations
    R'=|V_T|cos(theta)
    f_d=-2R'/lambda


    3. The attempt at a solution
    R^2=x^2+y^2 (x and y axes, x axis defined as direction ambulance is driving)
    implicitly derive
    2RR'=2xdx/dt+2ydy/dt
    y=4
    2RR'=2xdx/dt+8dy/dt
    dy/dt=0
    2RR'=2xdx/dt
    dx/dt=10
    2RR'=20x
    R'=10x/R

    Now what?
     
  2. jcsd
  3. Jul 18, 2014 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    OK so far.

    What is x(t)? You need to define a relationship between x and t and stick to it.
    What is r(x,y)? (Use r, not R. R implies a constant).
    Then come up with dr/dt in terms of v, t and y.
     
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