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10. We label the displacement vectors
G
A
,
G
B
and
G
C
(and denote the result of their vector
sum as
G
r
). We choose
east
as the
ˆ
i direction (+
x
direction) and
north
as the
ˆ
j direction
(+
y
direction) All distances are understood to be in kilometers.
(a) The vector diagram representing the motion is shown below:
ˆ
(3.1 km) j
ˆ
( 2.4 km)i
ˆ
( 5.2 km) j
A
B
C
=
=−
G
G
G
(b) The final point is represented by
ˆˆ
( 2.4 km)i ( 2.1 km)j
rABC
=++=−
+
−
GG
G
G
whose magnitude is
()
22
2.4 km
2.1 km
3.2 km
r
+
−
≈
G
.
(c) There are two possibilities for the angle:
1
2.1 km
tan
41 ,or 221
2.4 km
θ
−
§·
−
==
°
°
¨¸
−
©¹
.
We choose the latter possibility since
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 Spring '08
 Any
 Physics

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