Question

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.

Answer 1

Given:-

Proper time, t = 100 years

Speed of spaceship, v = \[\frac{60}{100}c= 0.60c\]

\[∆ t' = \frac{∆ t}{\sqrt{1 - \frac{v^2}{c^2}}}\]

\[ = \frac{100}{\sqrt{1 - \left( 0 . 60 \right)^2 \frac{c^2}{c^2}}}\]

\[ = \frac{100}{0 . 8} = 125 y\]

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