E(A)  =    5 GeV  =   8 x 10^(-10) J

We can figure out its gamma factor from

     
                                  2
        E(A)  =   gamma(A) * m * c


Plugging in m = 1.67 x 10^(-27) kg, we find


          gamma(A)  =  5.33     

We can then derive the velocity of proton A

          v(A)      =   0.982242 * c  =  2.94469 x 10^(8) m/s

and the time it takes for proton A to reach the Earth:

                          1.5 x 10^(11) m
          t(A)      =   ---------------------
                        2.94469 x 10^(8) m/s


                    =    509.4  seconds



       ---------------------

Now, let's look at the other proton, which has twice as much energy.

  E(B)  =    5 GeV  =   8 x 10^(-10) J

We can figure out its gamma factor from

          gamma(B)  =  10.66

We can then derive the velocity of proton B

          v(B)      =   0.995590 * c  =  2.98470 x 10^(8) m/s

and the time it takes for proton B to reach the Earth:

                          1.5 x 10^(11) m
          t(B)      =   ---------------------
                        2.98470 x 10^(8) m/s


                    =    502.6  seconds



  Therefore, the high-energy proton B reaches the Earth
slightly earlier than the low-energy proton A


      t(A) - t(B)   =   6.8  seconds