Question

You get pulled over for running a red light. You explain to the police officer that the light appeared green to you due to the Doppler effect. The police officer writes you a ticket for speeding instead. The fine is $100 for every 10km/hr over the speed limit of 60km/hr you were traveling. How much is the speeding ticket?

Answer 1

Answer:

$ 3085713685.71

Explanation:

$\lambda_0$ = Actual wavelength = 700 nm

$\lambda$ = Changed wavelength = 500 nm

Let the wavelength of red color be 700 nm and green be 500 nm

Change in wavelength is

$\Delta \lambda=700-500\\\Rightarrow \theta\lambda=200\ nm$

We have the relation

$\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}\\\Rightarrow v=\dfrac{\Delta\lambda}{\lambda_0}c\\\Rightarrow v=\dfrac{200}{700}\times 3\times 10^8\\\Rightarrow v=85714285.7143\ m/s$

The speed of the vehicle is 85714285.7143 m/s

$\dfrac{85714285.7143\times 3600}{1000}=308571428.571\ km/h$

By how much was the car speeding

$308571428.571-60=308571368.571\ km/h$

The number of 10 km/h in the above speed

$308571368.571\times\dfrac{1}{10}=30857136.8571$

Cost of the ticket

$30857136.8571\times 100=\ 3085713685.71$

The cost of the ticket is $ 3085713685.71

Answer 2

Answer:

not enough info

Explanation: