Question

A muon, with a lifetime of 2 x 10^-6 second in its frame of reference, is created in the upper atmosphere with a velocity of 0.998c toward the Earth. The lifetime of the muon, as measured by an observer on the Earth, is most nearly

A)3 x 10^-2s
B)3 x 10^-3s
C)3 x 10^-4s
D)3 x 10^-5s
E)3 x 10^-6s

Answer 1

The formula for time dilation is:\[\Delta t'=\frac{ 1 }{ \sqrt{1-\frac{ v ^{2} }{ c ^{2} }} }\Delta t\]where ∆t is time in the muon's frame of reference; and ∆t' is time in the observer's frame of reference.

Answer 2

Yes, lengthen its apparent lifetime by 1/sqrt(1-v^2/c^2))

Answer 3

is there a more simple formula to solve for the time? there are no calculators allowed and it seems like it would take too long to solve for the answer

Answer 4

That equation is as simple as it gets.

Answer 5

Note that you already given that:\[\frac{ v }{ c }=0.998\]and you thus know that \[\frac{ v ^{2} }{ c ^{2} }=0.998^{2}\]