Given:
The speed of the spaceship, v=0.75c
The time elapsed on the earth Δt₀=45 years=1.42×10⁹ s
To find:
The age of the twin that was sent into space.
Explanation:
The age of the twin sent into space is given by,
[tex]\Delta t_0=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]
On substituting the known values,
[tex]\begin{gathered} 1.42\times10^9=\frac{\Delta t}{\sqrt{1-\frac{0.75^2\times c^2}{c^2}}} \\ \implies\Delta t=1.42\times10^9\times\sqrt{1-0.75^2} \\ =0.94\times10^9\text{ s} \end{gathered}[/tex]
Converting it to years,
[tex]\Delta t=0.94\times10^9\text{ s}=29.8\text{ years}[/tex]
Final answer:
Thus the age of the twin that was sent into space is 29.8 years
