What is the Speed of the Speeder Relative to the Ground?

[arod2812]

Homework Statement

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 7.2 x 109 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 310 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground.

Homework Equations

WHAT do I do with the answer that I get for relative velocity?
DO I subtract the 27 m/s from the 12.92 that I got as an answer??

The Attempt at a Solution

fo=fs (1+Vrel/c)
Then I rearranged the equation to solve for the relative velocity.

I got: [(Change in frequency)/fs] * speed of light = relative velocity
which is 310 Hz/7.2E9 *3E8 = 12.92

 

[merryjman]

If the cop is moving at 27 m/s, and according to the cop the speeder is moving at 13 m/s, then what is the speeder's speed?? That, my friend, is an easy question. You've done the hard part already. Ponder this: 27-13 is 14 m/s, and 27+13 is 40 m/s. Convert these to mph and you tell me which one is more likely to represent a speeder.

 

[arod2812]

gotcha. thanks!