Answer:
$ 3085713685.71
Explanation:
[tex]\lambda_0[/tex] = Actual wavelength = 700 nm
[tex]\lambda[/tex] = Changed wavelength = 500 nm
Let the wavelength of red color be 700 nm and green be 500 nm
Change in wavelength is
[tex]\Delta \lambda=700-500\\\Rightarrow \theta\lambda=200\ nm[/tex]
We have the relation
[tex]\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[/tex]
The speed of the vehicle is 85714285.7143 m/s
[tex]\dfrac{85714285.7143\times 3600}{1000}=308571428.571\ km/h[/tex]
By how much was the car speeding
[tex]308571428.571-60=308571368.571\ km/h[/tex]
The number of 10 km/h in the above speed
[tex]308571368.571\times\dfrac{1}{10}=30857136.8571[/tex]
Cost of the ticket
[tex]30857136.8571\times 100=\$ 3085713685.71[/tex]
The cost of the ticket is $ 3085713685.71
