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Question
A person travels on a spaceship moving at a speed of 5c/13. (a) Find the time interval calculated by him between the consecutive birthday celebrations of his friend on the earth. (b) Find the time interval calculated by the friend on the earth between the consecutive birthday celebrations of the traveller.
Solution
Given: Speed of spaceship,
\[u = \frac{5c}{13}\]
(a) Proper time, t = 1 yr
Time interval calculated by him \[ = t' = \frac{t}{\sqrt{1 - u^2 / c^2}}\]
\[ = \frac{1 yr}{\sqrt{1 - \frac{25 c^2}{169 c^2}}}\]
\[ = \frac{13}{12} yr\]
Thus, the time interval calculated by him between the consecutive birthday celebrations of his friend on Earth is 13/12 years.
(b) The friend on Earth also considers the same speed, so the time interval calculated by him is also 13/12 years.
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