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 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 times 10^9 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 324 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground. Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of 0.957c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate? R = 3.4

Explanation / Answer

Using

Time dilation formula

t = t'/(1 - v2/c2)

8 breaths in 60 sec= 60/8 = 7.5 sec per breath

Now

t = (7.5)/(1 - 0.9572)

t = 25.85 sec

1/25.85 = 0.03868 breaths/s = 2.32 breaths/minute

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