A bean of unknown elementary particles travels at a speed of 2 x 10^8 m/s. Their average lifetime in the beam is measured to be 1.6 x 10^-8 s. Calculate their average lifetime when at rest.

Question

johnweldon1993 · Answer

hmm...it's definitely been awhile since I've done these...I believe you start with the equation

$$t = \frac{ t_o }{ \sqrt{1-\frac{ v^2 }{ c^2 }} }$$

We want t_o so rearranging we have

$$t_o = t \sqrt{1-\frac{ v^2 }{ c^2 }}$$

You know v = speed it's traveling at
t = average lifetime
c = speed of light

so replace v with 2 x 10^8
replace t with 1.6 x 10^-8
and replace c with 3.0 x 10^8

to get

$$(1.6 * 10^{-8})\sqrt{1-\frac{ (2.0 * 10^8) }{ (3.0 * 10^8 )}^2}$$

*and yes that ^2 is outside of that whole fraction...it should be [(2.0 * 10^8)/(3.0 * 10^8)] all ^2

So can you solve that?

anonymous · Answer

thank you

johnweldon1993 · Answer

no problem...I believe that is correct...better you double check my work...as stated it HAS been a while since doing those types of problems

anonymous · Answer

can you help with another problem