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

$ 3085713685.71

Step-by-step 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

`(\Delta\lambda)/(\lambda_0)=(v)/(c)\\\Rightarrow v=(\Delta\lambda)/(\lambda_0)c\\\Rightarrow v=(200)/(700)* 3* 10^8\\\Rightarrow v=85714285.7143\ m/s`

The speed of the vehicle is 85714285.7143 m/s

`(85714285.7143* 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*(1)/(10)=30857136.8571`

Cost of the ticket

`30857136.8571* 100=\$ 3085713685.71`

The cost of the ticket is $ 3085713685.71