Relativity

Question 5 in the 2003 HSC Physics examination was a multiple choice question on time dilation and length contraction. Unfortunately, no correct answer was given as an alternative. Students doing revision often ask about this question. As the mark for the question was apparently not included in the final mark it could probably be ignored. However, an answer involves taking into account the travel time of the light coming from the Earth as the question says "when seen from the astronaut's spaceship"...seen implying making an observation using light .  From the point of view of the astronaut in the spaceship the Earth is moving away at 0.8c. The time for the journey in the reference frame of the spaceship is 10 years. The distance of the journey in the reference frame of the spaceship is 8 light years and so a ray of light would take a time interval of 2 years in the spaceships reference frame to reach the spaceship. To determine the corresponding time interval shown by the clock on the Earth we solve the time dilation equation for t0 putting tv as 2 and v as 0.8c. This is because the astronaut considers the Earth to be moving away carrying its clock with it. This works out to be 1.2 years.

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