Vector Addition

1
Vector Addition

• Graphical Approach

2
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
E
W
S
3
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
9 km (18 cm)
campsite
E
W
35
S
4
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
6 km (12 cm)
70
9 km (18 cm)
campsite
E
W
35
S
5
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
6
Vector Addition

• Analytical Approach

7
Review of Trigonometry
Z (X2 Y2)1/2
cos ? X/Z so X Z cos ?
Z
Y
sin ? Y/Z so Y Z sin ?
?
X
tan ? Y/X so ? tan-1(Y/X)
8
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
r1x 9.0 cos(35) 7.4 km
r1y 9.0 sin(35) 5.2 km
5.2 km
9 km
campsite
E
W
35
7.4 km
S
9
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
r2x 6.0 cos(70) 2.1 km
r2y 6.0 sin(70) 5.6 km
r2 6 km
5.6 km
70
2.1 km
5.2 km
9 km
campsite
E
W
7.4 km
35
S
10
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
N
rRx ?
rRy ?
5.6 km
70
2.1 km
rRy
5.2 km
rRx
campsite
E
W
7.4 km
35
S
11
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?
12
A hiker starts at his campsite and travels 9.0 km
in a direction 35 north of east. Next, he
changes direction so that he is heading 70 north
of west and he continues an additional 6.0 km.
How far and in what direction from his campsite
is he?