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26. (a) From Table 372, we find
()
( )
2
[400 m
(1.00
s)]
400 m (299.8 m)
1
xx
v
t
x
c
t
c
γ
γβ
β
µ
′
∆ = ∆−∆ = ∆− ∆ =
−
−
=
−
(b) A plot of
'
x
∆
as a function of
with 0
0.01
<
<
is shown below:
(c) A plot of
'
x
∆
as a function of
with 0.1
1
<
<
is shown below:
(d) To find the minimum, we can take a derivative of
∆
x
′
with respect to
β
, simplify, and
then set equal to zero:
23
/
2
2
0
(1
)
1
dx
d
x ct
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 Spring '08
 Any
 Physics

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