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

Hint: First of all you could note down the given quantities like the average lifespan of the person in the rest frame and the velocity of the spaceship. As there is a relative motion between the two frames the concept of time dilation comes into picture. Now, you could recall the expression for dilated time and hence find the answer.
Formula used:
Time dilation,
$t'=\dfrac{t}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$

Complete answer:
In the question, we are given that a person lives on an average of 100years in his rest frame. Now we have another spaceship that is moving with a velocity that is 60% that of the speed of light. If this same person was to spend his entire lifetime in this spaceship, we are supposed to find his lifetime in this new moving frame.
Let t be the lifespan of the person in the rest frame and t’ be the lifespan of the person in the moving frame. Then, from the concept of time dilation we have that,
$t'=\dfrac{t}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$
Where,
$v=\dfrac{60}{100}c=0.6c$
$t=100years$
Substituting these values,
$t'=\dfrac{100}{\sqrt{1-{{\left( \dfrac{0.6c}{c} \right)}^{2}}}}$
$\Rightarrow t'=\dfrac{100}{\sqrt{0.64}}=\dfrac{100}{0.8}$
$\therefore t'=125years$
Therefore, we found the lifespan of the person in the spaceship moving at a speed of 60% that of c to be 125years.

Note:
The concept of time dilation simply implies the difference that is observed between the time that is shown by the two clocks. This could be observed as the result of relative velocities between them or may be due difference in gravitational potential between their respective locations. In the example given here it is due to the relative velocities of the two bodies.