Answer:
v = 0.9798*c
Explanation:
E0 = 105 MeV
The mass of a muon is
m = 1.78 * 10^-30 kg
The kinetic energy is:
[tex]Ek = \frac{E0}{\sqrt{1 - \frac{v^2}{c^2}}}-E0[/tex]
The kinetic energy is 4 times the rest energy.
[tex]4*E0 = \frac{E0}{\sqrt{1 - \frac{v^2}{c^2}}}-E0[/tex]
[tex]4 = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}-1[/tex]
[tex]5 = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]
[tex]\sqrt{1 - \frac{v^2}{c^2}} = \frac{1}{5}[/tex]
[tex]1 - \frac{v^2}{c^2} = \frac{1}{25}[/tex]
v^2 / c^2 = 1 - 1/25
v^2 / c^2 = 24/25
v^2 = 24/25 * c^2
v = 0.9798*c
