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 : $v = 0.6 c$
Time spend in the spaceship (rest frame) $τ = 100$ years
Time passed on earth $t = \frac{τ}{\sqrt{1 - (v / c)^{2}}}$
$∴$ $t = \frac{100}{\sqrt{1 - (0.6)^{2}}}$ $⟹ t = 125$ years

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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.

Given : v=0.6cTime spend in the spaceship (rest frame) τ=100 yearsTime passed on earth t=τ√1−(v/c)2∴ t=100√1−(0.6)2 ⟹t=125 years

Given : $v = 0.6 c$
Time spend in the spaceship (rest frame) $τ = 100$ years
Time passed on earth $t = \frac{τ}{\sqrt{1 - (v / c)^{2}}}$
$∴$ $t = \frac{100}{\sqrt{1 - (0.6)^{2}}}$ $⟹ t = 125$ years