Answer:
The velocity is  [tex]v= 17320.01 m/s[/tex]
Explanation:
In order to provide solution to this question we are going to be making use of the time dilation equation which is mathematically represented as
            [tex]\Delta t' = \frac{\Delta t}{\sqrt{1- \frac{v^2}{c^2} } }[/tex]
Where [tex]\Delta t'[/tex] is the desired time to achieve the time travel which is give from the question as
       [tex]\Delta t' = 1 \ month =1 *30 *24*60*60 =2.592*10^6 sec[/tex]
 and  [tex]\Delta t[/tex] is the actual earth time which is given from the question as
       [tex]\Delta t = 11 \ years = 11 *12*30*24*60*60 = 3.2421*10^8sec[/tex]
 and c is the speed of light with a value of  [tex]c = 3.0*10^8 m/s[/tex]
 and  v  is the speed we need to obtain
   Now making v the subject of the formula
           [tex]\Delta t' * \sqrt{1 - \frac{v^2}{c^2} } = \Delta t[/tex]
              [tex]\sqrt{1 - \frac{v^2}{c^2} } = \frac{\Delta t}{\Delta t'}[/tex]
          [tex]1 - \frac{v^2}{c^2} = (\frac{\Delta t}{\Delta t'})^2[/tex]
          [tex]\frac{v^2}{c^2} = 1 - (\frac{\Delta t}{\Delta t'})^2[/tex]
         [tex]v^2 = (1 - (\frac{\Delta t}{\Delta t'})^2)c^2[/tex]
         [tex]v = \sqrt{ (1 - (\frac{\Delta t}{\Delta t'})^2)c^2}[/tex]
Now substituting values
        [tex]v = \sqrt{(1- (\frac{2.592*10^6}{3.421*10^8} )^2) * 3.0*10^8}[/tex]
         [tex]v= 17320.01 m/s[/tex]
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