Multiple-Concept Example 6 reviews the concepts that play a role in this problem
ID: 1451372 • Letter: M
Question
Multiple-Concept Example 6 reviews the concepts that play a role in this problem. A speeder is pulling directly away and increasing his distance from a police car that is moving at 23 m/swith respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 7.1 × 109 Hz. The wave reflects from the speeder’s car and returns to the police car, where its frequency is measured to be 400 Hz less than the emitted frequency. Find the speeder’s speed with respect to the ground
Chapter 24, Problem 36 GO Multiple-Concept Example 6 reviews the concepts that play a role in this problem. A speeder is pulling directly away and increasing his distance from a police car that is moving at 23 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 7.1 x 109 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 400 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground Vspeeder Number Units the tolerance is +/-2%Explanation / Answer
Given,
Vp = 23 m/s ; f1 = 7.1 x 109 Hz ;
f2 = f1 (1 - Vr/c)2
sqrt (f2/f1) = (1 - Vr/c)
Vr/c = 1 - sqrt (f2/f1)
Vr/c = 1 - sqrt [ (7.1 x 109 - 400) / 7.1 x 109] = 2.2 x 10-8
Vr = 2.2 x 10-8 x c = 2.35 x 10-8 x 3 x 108 = 7.05 m/s
Hence, Vr = 7.05 m/s.
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