A passenger on a fictional high-speed spaceship traveling between Earth and Jupi

Question

A passenger on a fictional high-speed spaceship traveling between Earth and Jupiter at a steady speed of 0.75c reads a magazine which takes 10.0 min according to her watch. How long does this take as measured by Earth-based clocks?

How do you solve to get D as the correct answer?

l) A passenger on a fictional high-speed spaceship traveling between Earth and Jupiter at a steady speed of 0.75c reads a magazine which takes 10.0 min according to her watch. How long does this take as measured by Earth-based clocks? A) 7.50 min B 10.0 min C) 13.3 min DO 15.1 min E) None of the above

Explanation / Answer

APPROACH (a) The time interval in one reference frame is related to the time interval in the other . At constant speed, distance is Because there are two time intervals ( and ) we will get two distances, one for each reference frame.

SOLUTION (a) The given 10.0-min time interval is the proper time —starting and finishing the magazine happen at the same place on the spaceship.

(a) The given 10.0-min time interval is the proper time t starting and finishing the magazine happen at the same place on the spaceship. Earth clocks measure

t = t' / (1-(v2/c2))^1/2

= 10 min/ (1 -(0.75)2)^1/2

= 15.1 minutes

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