Calculating Doppler Shift from Ambulance Movement

[jamcintyre1]

1. Homework Statement
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. Homework 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?

 

[rude man]

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.