What's the answer to this mass-energy problem?

Question

A particular particle has mass-energy 494 MeV and decays in 1.2 x 10 ^ -8 s in its rest frame. What is the enrgy in the frame of the lab if it travels 10.0 m before decaying?:

Answer 1

tau=1.2 x 10^-8 sec
t=gamma tau
gamma= 1/sqrt(1-beta^2)
c= 299,792,458 m/s
10=velocity x t = (beta c) (gamma tau)

solve for beta
beta/ sqrt (1-beta^2) = 10/(c tau) = call it x = 2.784

b^2=x^2-x^2b^2
b^2(1+x^2)=x^2
beta = sqrt(x^2/(1+x^2))=.941
gamma= 2.96

energy in the lab frame is gamma m = 1462 MeV

Answer 2

I voted for electron1's answer above, yet i think that dropping a million kg demands which you carry out purely 25% of the sensible artwork, not 4 hundred%. So i think of you will divide that answer by using sixteen (4x4). nevertheless an extremely long term. The "binding means" of chemical bonds is fullyyt somewhat measureable (in hydrogen), so there is reason to have self belief that it is there for different, weaker bonds... in spite of if this is doing sensible artwork, or "staying alive". *Measuring* the mass loss in a human could be impossible, of direction.