Final answer:
To calculate the vehicle's speed using the Doppler effect and given the frequencies of the radar, we use the adjusted Doppler shift equation and solve for velocity. The change in frequency is attributed to the radar waves reflecting off the vehicle and is used to determine the required velocity.
Step-by-step explanation:
The question pertains to calculating the velocity of a vehicle using the Doppler effect for radar waves. Given the frequency of the outgoing radar at 100 GHz and the frequency of the returning echo being 15.0 kHz higher, we need to use the Doppler shift equation adapted for electromagnetic waves:
f' = f(1 + v/c), where f' is the observed frequency, f is the emitted frequency, v is the velocity of the vehicle relative to the stationary radar, and c is the speed of light. The change in frequency due to the Doppler effect is double because it accounts for the radar signal bouncing off the vehicle and returning to the source.
First, we identify the change in frequency (Δf) which is a result of the radar waves bouncing off the moving vehicle: Δf = 2 * (f' - f). Then, the velocity (v) of the vehicle can be extracted using the rearranged formula: v = Δf * (c / (2 * f)).
Using the provided data: the emitted frequency (f) of the radar is 100 GHz or 100*109 Hz, the observed frequency difference is 15.0 kHz or 15*103 Hz, and the speed of light (c) is a constant 3*108 m/s. Inserting these values into the equation gives us the speed of the vehicle.