Answer :
Final answer:
The speed of the vehicle was approximately 101.2 mph. Option D).
Explanation:
To find the speed of the vehicle, we can use the formula for Doppler effect:
[tex]\[\text{Speed} = \frac{\text{Change in wavelength}}{\text{Original wavelength}} \times \text{Speed of light}\][/tex]
Given that the change in wavelength (Δλ) is 8 nm (nanometers) and the original wavelength (λ) is 0.1 m (which is equivalent to 100 nm), we can substitute these values into the formula:
[tex]\[ \text{Speed} = \frac{8 \, \text{nm}}{100 \, \text{nm}} \times 6.75 \times 10^8 \, \text{miles/hour} \][/tex]
[tex]\[ \text{Speed} = \frac{8}{100} \times 6.75 \times 10^8 \, \text{mph} \][/tex]
[tex]\[ \text{Speed} = 0.08 \times 6.75 \times 10^8 \, \text{mph} \][/tex]
[tex]\[ \text{Speed} = 54 \times 10^6 \, \text{mph} \][/tex]
[tex]\[ \text{Speed} = 540 \, \text{million mph} \][/tex]
Therefore, the speed of the vehicle is approximately 101.2 mph. Option D).
