Answer:
0.99641 c
Explanation:
[tex]\Delta t'[/tex] = 130 years
[tex]\Delta t[/tex] = 11 years
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
Time dilation is given by
[tex]\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[/tex]
The speed of the rocket is 0.99641 c
