SAT Subject Physics Practice Question 304: Answer and Explanation

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Question: 304

75. Five identical spaceships take off from Planet X, and each passes by Planet Y at a constant speed on its way to Planet Z. A science station on Planet Y observes them passing by. The spaceship traveling at which of the following speeds would be observed to have the greatest length?

A. 6 × 107 m/s
B. 9 × 107 m/s
C. 1 × 108 m/s
D. 1.5 × 108 m/s
E. 2 × 108 m/s

Correct Answer: A

Explanation:

The faster a spaceship passes by the station, the shorter its length is observed to be. This is because as v increases, the relativistic factor γ increases, so the amount of length contraction increases. Therefore, the smaller the v, the smaller the value of γ, and the longer the ship will be observed to be. Of the choices given, the speed in A is the smallest. (Note that the spaceship traveling at the speed given in E will be observed to be the shortest as it passes by the station.)

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