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57. (a) We compute
γ
=
1
p
1
−
(0
.
9990)
2
=22
.
4
Now, the length contraction formula (Eq. 3813) yields
L
=
2
.
50 m
γ
=0
.
112 m
.
(b) (c) and (d) We assume our spacetime coordinate origins coincide and use the Lorentz transforma
tions (Eq. 3820, but with primes and nonprimes swapped, and
v
→−
v
). Lengths are in meters
and time is in nanoseconds (so that
c
=0
.
2998 in these units).
x
α
=
γ
(4
.
0+(0
.
9990
c
)(40)) = 357
t
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 Fall '08
 SPRUNGER
 Physics

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