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

A speeder is pulling directly away and increasing his distance from a police car that is moving at 27 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 6.00 109 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 316 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground.
_______m/s

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Answer #1

Given

speed of police car vp = 27.0 m/s
frequency of source fs = 6. x 109 Hz
the difference between frequency of source and observer fs - fo = 316 Hz
  The relative speed is
      vrel = ( fs-fo / 2fs) * c
            = ( 316 / 2 * 6. x 109 ) * 3 x 108
            = 7.9 m/s
the relative speed is the difference between speed of police car and speeder

         Vrel = vs - vp
==> vs = vrel + vp
            = 7.9 + 27
            = 34.9 m/s

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