If a person lives on the average 100 years in his rest frame, how long does he live in the earth frame if he spends all his life on a spaceship going at 60% of the speed of light.

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Solution

Given:
Proper time, t = 100 years
Speed of spaceship, v = $\frac{60}{100} c$ = 0.60c

$∆ t' = \frac{∆ t}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{100}{\sqrt{1 - {(0.60)}^{2} \frac{c^{2}}{c^{2}}}} = \frac{100}{0.8} = 125 y$

Thus, the person lives for 125 years in the Earth frame.

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