## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

We can find the speed of the car as: $\lambda' = \lambda_0~\frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}$ $\frac{\lambda'}{\lambda_0} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}$ $(\frac{\lambda'}{\lambda_0})^2 = \frac{1-v/c}{1+v/c}$ $(\frac{\lambda'}{\lambda_0})^2(c+v) = c-v$ $v~[1+(\frac{\lambda'}{\lambda_0})^2] = [1-(\frac{\lambda'}{\lambda_0})^2]~c$ $v = \frac{1-(\frac{\lambda'}{\lambda_0})^2}{1+(\frac{\lambda'}{\lambda_0})^2}~c$ $v = \frac{1-(\frac{540~nm}{650~nm})^2}{1+(\frac{540~nm}{650~nm})^2}~(3.0\times 10^8~m/s)$ $v = 5.5\times 10^7~m/s$ We then convert the speed to km/h: $v = (5.5\times 10^7~m/s)(\frac{1~km}{1000~m})(\frac{3600~s}{1~h})$ $v = 2.0\times 10^8~km/h$ The speed of the car is $2.0\times 10^8~km/h$. Since the fine is 1 dollar for every 1 km/h over the speed limit of 50 km/h, the fine is $2.0\times 10^8~dollars$ which is 200 million dollars.