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8. Let
w
v
be the speed of the wind and
c
v
be the speed of the car.
(a) Suppose during time interval
1
t
, the car moves in the same direction as the wind.
Then its effective speed is
,1
eff
c
w
vv
v
=+
, and the distance traveled is
,1 1
1
()
eff
c
w
dvt vvt
==
+
. On the other hand, for the return trip during time interval
t
2
, the
car moves in the opposite direction of the wind and the effective speed would be
,2
eff
c
w
v
=−
. The distance traveled is
,2 2
2
eff
c
w
−
. The two expressions can
be rewritten as
12
and
cw
dd
tt
+=
−=
Adding the two equations and dividing by two, we obtain
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 Spring '06
 Stoler
 Physics

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