5. In the laboratory, it travels a distance d = 0.00105 m = vt, where v = 0.992c and t is the time measured

on the laboratory clocks. We can use Eq. 38-7 to relate t to the proper lifetime of the particle t

0

:

t =

t

0

1

− (v/c)

2

=

⇒ t

0

= t



1

−



v

c



2

=

d

0.992c

1

− 0.992

2

which yields t

0

= 4.46

× 10

−13

s.