Question

A speeder is pulling directly away and increasing his distance from a police car that is moving at 29 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 7.00 109 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 326 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground.

Answer 1

As mentioned in the problem, the measured frequency is 326 Hz less than the emitted frequency.

This means, in one second the car would have gained a distance of 326 wavelengths of the radar from the police car.

Now, each wavelength has a length of c/f where c is the speed of light.

Therefore, the car would gain (326 * 3.0 * 10^8) /( 7.00 * 10 ^9) = 13.97 metres in one second.  

Therefore, the speeder's speed with respect to the ground = 29 m/s + 13.97 m/s

= 42.97 m/s (Answer)

Hope, you understand the solution !