In the MichelsonMorley experiment what would uc have to be t

In the Michelson-Morley experiment what would u/c have to be to make t_2 exactly 1 percent larger than t_1? For this value of u/c, what is t_1 (in seconds) if the length. L, were exactly 1 meter? Use at least six significant digits in the computation, to appreciate the time differences.

Solution

      if t 2 and t1 are conencted by

                                           t2 = t1 / sqrt (1-(u/c)^2)

      t2 is 1% larger than t1 =>    t2 = t1 * 1.01      

                     => 1 / sqrt (1-(u/c)^2) = 1.01

                                                          using tailors expansion 1 / sqrt (1-x^2) = 1+0.5x^2

                                       1 + 0.5(u/c) = 1.01 => u/c = 0.01/0.5 => u/c = 0.02