Patrol Infrared

Please help with physics problem!?

A) You're caught running a red light on Hwy 31. Attempting to impress the skeptical patrol officer with your physics knowledge, you claim that you were traveling so fast that the red light (692 nm) appeared yellow (579 nm) to you.
How fast would you have been traveling (in mi/hr) if that had been the case?

B) Multiple Choice
If you had been traveling that fast and the light actually was yellow, what color would it have seemed to you?

yellow
blue
red
invisible (ultraviolet or infrared)
green
orange

A) From the Doppler eqn we have f = sqrt((c + u)/(c - u))*f0 and since f = c/λ we have

1/λ = 1/λ0*sqrt((c + u)/(c - u)) Solving (λ0/λ)^2 = (c + u)/ (c - u)

(λ0/λ)^2*(c - u) = c + u

so (1 + (λ0/λ)^2) u = ((λ0/λ)^2 - 1)*c

So u = ( ((λ0/λ)^2 - 1)*c)/(1 + (λ0/λ)^2) = ((692/579)^2 - 1)*3.0x10^8/(1 + (692/579)^2) =

5.29x10^7m/s = 1.18x10^8mph

B) Here we have 1/λ = 1/λ0*sqrt((c + u)/(c - u))

So λ = λ0/sqrt((c + u)/(c - u)) = 579/sqrt((3.0x10^8 + 5.29x10^7)/(3.0x10^8 - 5.29x10^7))

So λ = 484nm This corresponds to blue light

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