Question

A particle is traveling with respect to an observer such that its Einsteinian energy is 2.32 times its rest energy. How fast is it moving with respect to the observer? Answer in units of the speed of light, and to three decimal places, for example if the answer is 0.123 c report 0.123.

Answer 1

Write the equation for the Relativistic energy.

                  Eγ = γmc2

Given in the problem

Eγ = 2.32Eo =2.32mc2

Write the equation for the relativistic factor

γ = 1/ √ [1-(v/c)2] ......... (1)

      2.32mc2=   γmc2

           γ = 2.32

Use equation (1)

      1/ √ [1-(v/c)2] =2.32

      1 /  [1-(v/c)2]   = 5.38

          [1-(v/c)2] = 1/5.38

         (v/c)2= 1-1/5.38

             (v/c)2= 0.814

v/c = 0.9

v = 0.9c

The speed of the particle relative to obserber is 0.9