Question

At what speed, at a fraction of c, must rocket travel on a journey to and from a distant star so that the astronaut's age 11 years while the Mission Control workers on earth age 130 years?

Answer 1

Answer:

0.99641 c

Explanation:

$\Delta t'$ = 130 years

$\Delta t$ = 11 years

c = Speed of light = $3\times 10^8\ m/s$

Time dilation is given by

$\Delta t'=\dfrac{\Delta t}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \sqrt{1-\dfrac{v^2}{c^2}}=\dfrac{\Delta t}{\Delta t'}\\\Rightarrow 1-\dfrac{v^2}{c^2}=\dfrac{\Delta t^2}{\Delta t'^2}\\\Rightarrow \dfrac{v}{c}=\sqrt{1-\dfrac{\Delta t^2}{\Delta t'^2}}\\\Rightarrow \dfrac{v}{c}=\sqrt{1-\dfrac{11^2}{130^2}}\\\Rightarrow \dfrac{v}{c}=0.99641\\\Rightarrow v=0.99641c$

The speed of the rocket is 0.99641 c