Calculating the Fine for Speeding Using the Doppler Effect Equation

[asdf1]

There's a speeding ticket problem, and I'm don't know to start thinking about how to solve the problem~
"A driver is caught going through a red light. The driver claims to the judge that the color she actually saw was green (f=5.6*10^14 hz) because of the doppler effect. The judge accepts this explanation and instead fines her for speeding at the rate of $1 for each km/h she exceeded the speed limit of 80km/h. What was the fine?

 

[Hurkyl]

Can you set any intermediate goals?
Is there anything you can figure out from the given information?
What pieces of information would allow to determine the answer?

Have you asked yourself any of these questions yet?

 

[asdf1]

Yes. Because that's an example in a textbook. There's the solution, but I don't know why the solution solves the problem that way.

 

[Jelfish]

You want to know the fine amount. You know how much she'll pay per km/h she exceeds the speed limit. So what information do you need in order to find out how much she'll be fined?

 

[asdf1]

how much she overspeed?

 

[Jelfish]

Yes - now in order to find that, you need to know what her speed was. The only information you have is that her supposed red light looked green because of the doppler effect. If you've learned about the doppler effect, you should know an equation that tells you how fast she needed to go for that to happen. Then find out how much faster it was than 80km/h and you have your answer.

 

[asdf1]

oh, i see!
Thank you very much!

 

[asdf1]

hmm... i tried solving this equation using the doppler effect equation: f`=f((c+v)/c) where v=speed of observer and c = speed of light
so
5.6*10^14=4.8*10^14(3*10^8+v)/(3*10^8)
=> 7/6*3*10^8=3*10^8+v
=> v=(1/6)*3*10^8
but that's not right, because the correct answer should be 4.59*10^7
does anybody know what went wrong?