16
Chapter 1
1.31.
I
DENTIFY
:
Draw each subsequent displacement tail to head with the previous displacement. The resultant
displacement is the single vector that points from the starting point to the stopping point.
S
ET
U
P
:
Call the three displacements
A
"
,
B
"
, and
C
"
. The resultant displacement
R
"
is given by
R = A+ B + C
"
"
"
"
.
E
XECUTE
:
The vector addition diagram is given in Figure 1.31. Careful measurement gives that
R
"
is
7.8 km, 38 north of east
#
.
E
VALUATE
:
The magnitude of the resultant displacement, 7.8 km, is less than the sum of the magnitudes of the
individual displacements, 2.6 km
4.0 km
3.1 km
+
+
.
Figure 1.31
1.32.
I
DENTIFY
:
Draw the vector addition diagram, so scale.
S
ET
U
P
:
The two vectors
A
"
and
B
"
are specified in the figure that accompanies the problem.
E
XECUTE
:
(a)
The diagram for
C = A+ B
"
"
"
is given in Figure 1.32a. Measuring the length and angle of
C
"
gives
9.0 m
C
=
and an angle of
34
θ
=
°
.
(b)
The diagram for
−
D = A
B
"
"
"
is given in Figure 1.32b. Measuring the length and angle of
D
"
gives
22 m
D
=
and
an angle of
250
θ
=
°
.
(c)
(
)
−
−
−
A
B =
A+ B
"
"
, so
−
−
A
B
"
"
has a magnitude of 9.0 m (the same as
A+ B
"
"
) and an angle with the
x
+
axis
of 214
°
(opposite to the direction of
A+ B
"
"
).
(d)
(
)
−
−
−
B
A =
A
B
"
"
"
"
, so
−
B
A
"
"
has a magnitude of 22 m and an angle with the
x
+
axis of 70
°
(opposite to the
direction of
−
A
B
"
"
).
E
VALUATE
:
The vector
−
A
"
is equal in magnitude and opposite in direction to the vector
A
"
.
Figure 1.32
1.33.
I
DENTIFY
:
Since she returns to the starting point, the vectors sum of the four displacements must be zero.
S
ET
U
P
:
Call the three given displacements
A
"
,
B
"
, and
C
"
, and call the fourth displacement
D
"
.
0
A+ B + C + D =
"
"
"
"
.
E
XECUTE
:
The vector addition diagram is sketched in Figure 1.33. Careful measurement gives that
D
"
is144 m, 41 south of west.
#
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17
E
VALUATE
:
D
"
is equal in magnitude and opposite in direction to the sum
A+ B + C
"
"
"
.
Figure 1.33
1.34.
I
DENTIFY
and
S
ET
U
P
:
Use a ruler and protractor to draw the vectors described. Then draw the corresponding
horizontal and vertical components.
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 Spring '06
 Buchler
 Physics, Addition, Vector Space, Force, ax

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