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16. The “coincidence” of
x = x'
= 0 at
t = t'
= 0 is important for Eq. 3721 to apply
without additional terms. We label the event coordinates with subscripts: (
x
1
,
t
1
) = (0, 0)
and (
x
2
,
t
2
) = (3000 m, 4.0
×
10
–6
s).
(a) We expect (
x'
1
,
t'
1
) = (0, 0), and this may be verified using Eq. 3721.
(b) We now compute (
x'
2
,
t'
2
), assuming
v
= +0.60
c
= +1.799
×
10
8
m/s (the sign of
v
is
not made clear in the problem statement, but the Figure referred to, Fig. 379, shows the
motion in the positive
x
direction).
86
3
2
22
68
6
2
3000 m (1.799 10 m/s)(4.0 10
s)
2.85 10 m
1
1 (0.60)
4.0 10
s (0.60)(3000 m)/(2.998 10 m/s)
2.5 10
s
1
1 (0.60)
xv
t
x
tx
c
t
β
−
−
−
−−
×
×
′
==
=
×
−×
−
×
′
=
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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