Answer
(a) $E = 532.65~MeV$
(b) The total energy in the muon's frame is $106~MeV$
Work Step by Step
(a) We can find the total energy in the Earth observer's frame:
$E = \gamma~m~c^2$
$E = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}~m~c^2$
$E = \frac{1}{\sqrt{1-\frac{(0.980~c)^2}{c^2}}}~(106~MeV)$
$E = (5.025)(106~MeV)$
$E = 532.65~MeV$
(b) In the muon's frame, the muon is at rest. Therefore, the total energy in the muon's frame is $106~MeV$
