A speeder is pulling directly away and increasing his distance from a police car

Question

A speeder is pulling directly away and increasing his distance from a police car that is moving at 26.0 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 6.97E+9 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 331 Hz less than the emitted frequency. Calculate the speeder's speed with respect to the ground. 

Explanation / Answer

Given that vp = 26.0 m/s fs = 6.97 x 109 Hz fs - fo = 331 Hz vs = ? The relative speed is       vrel = ( fs-fo / 2fs) * c             = ( 331 / 2 * 6.97 x 109 ) * 3 x 108             = 7.12 m/s So that     We know that          Vrel = vs - vp ==> vs = vrel + vp             = 7.12 + 26             = 33.12 m/s

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