2008 HSC

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2008 HSC

Post by noahyim »


Sorry for asking so many questions - the syllabus is really starting to break and crumple apart for me.
There is a question in the 2008 paper I disagree with, and I'm wondering if I'm right.

5) A spaceship is travelling away from Earth at 1.8 × 108 ms–1. The time interval between consecutive ticks of a clock on board the spaceship is 0.50 s. Each time the clock ticks, a radio pulse is transmitted back to Earth.
What is the time interval between consecutive radio pulses as measured on Earth?

It's a multiple choice question. I believe that the answer to this question should be 0.5s, since it's being measured on Earth. However, the answer says that it is 0.63s. I thought that this would only be true if the question asked - "what is the time interval between pulses on Earth as measured from the spaceship", or "What is the time interval between pulses on the spaceship as measured from Earth". Is my understanding of special relativity correct?

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Re: 2008 HSC

Post by joe »

0.5 s is the time interval on the clock on the ship. For an earth observer, that time is dilated. See
which explains time dilation with animations.

However, there's a complication. 0.63 s is the answer you'd get if the ship happened to be travelling at right angles to its displacement from the Earth, and was many light seconds away. But in this question, the ship is travelling 'away from Earth'. So it depends on what is meant by 'as measured on Earth'. If it means the time between clicks from the clock being received on Earth, one would need to use the relativistic Doppler effect. If it means the time calculated on Earth after accounting for the Doppler shift, then that is a different answer. I guess that the latter is intended.
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