Preview Extract

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Graphical Addition: Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If
these two vectors are added together, the magnitude of the sum
A) could be as small as 2.0 m or as large as 12 m.
B) is equal to 12 m.
C) is equal to 8.6 m.
D) is equal to 2.0 m.
Answer: A
2) Graphical Addition: Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one
of the following is a possible value for the magnitude of the resultant?
A) 80 mm
B) 20 mm
C) 10 mm
D) 40 mm
Answer: D
3) Graphical Addition: The magnitude of the resultant of two vectors cannot be less than the
magnitude of either of those two vectors.
A) True
B) False
Answer: B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) Graphical Addition: A student adds two displacement vectors that have the magnitudes of 12.0 m
and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?
Answer: Between 7.0 m and 17.0 m
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5) Graphical Addition: If A + B = C and their magnitudes are given by A + B = C, then the vectors
A and B are oriented
A) parallel to each other (in the same direction).
B) perpendicular relative to one other.
C) antiparallel to each other (in opposite directions).
D) It is impossible to know from the given information.
Answer: A
6) Graphical Addition: If A – B = 0, then the vectors A and B have equal magnitudes and are
directed in the same direction.
A) True
B) False
Answer: A
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7) Graphical Addition: If three vectors add to zero, they must all have equal magnitudes.
A) True
B) False
Answer: B
8) Graphical Addition: The sum of two vectors of fixed magnitudes has the greatest magnitude when
the angle between these two vectors is
A) 270ยฐ.
B) 180ยฐ.
C) 60ยฐ.
D) 0ยฐ.
E) 90ยฐ.
Answer: D
9) Graphical Addition: The sum of two vectors of fixed magnitudes has its minimum magnitude when
the angle between these vectors is
A) 90ยฐ.
B) 270ยฐ.
C) 0ยฐ.
D) 180ยฐ.
E) 360ยฐ.
Answer: D
10) Graphical Addition: Vectors M and N obey the equation M + N = 0. These vectors satisfy which
one of the following statements?
A) Vectors M and N have the same magnitudes.
B) Vectors M and N are at right angles to each other.
C) Vectors M and N point in the same direction.
D) The magnitude of M is the negative of the magnitude of N .
Answer: A
11) Graphical Addition: Consider two vectors A and B shown in the figure. The difference A – B is
best illustrated by
A) choice (a)
B) choice (b)
C) choice (c)
Answer: C
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D) choice (d)
12) Graphical Addition: Consider two vectors A and B shown in the figure. The difference A – B is
best illustrated by
A) choice (a)
B) choice (b)
C) choice (c)
D) choice (d)
Answer: B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
13) Graphical Addition: Refer to the figure, which shows four vectors M , N , S , and T .
(a) Vector S as expressed in terms of vectors M and N is given by
A) M + N .
B) M – N .
C) N – M .
(b) Vector T as expressed in terms of vectors M and N is given by
A) M + N .
B) M – N .
C) N – M .
Answer: (a) B (b) A
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
14) Components: If a vector pointing upward has a positive magnitude, a vector pointing downward has
a negative magnitude.
A) True
B) False
Answer: B
15) Components: If a vector’s components are all negative, then the magnitude of the vector is negative.
A) True
B) False
Answer: B
16) Components: The magnitude of a vector can never be less than the magnitude of any of its
components.
A) True
B) False
Answer: A
17) Components: The magnitude of a vector an only zero if all of its components are zero.
A) True
B) False
Answer: A
18) Components: If a vector A has components Ax 0, then the angle that this vector
makes with the positive x-axis must be in the range
A) 0ยฐ to 90ยฐ.
B) 90ยฐ to 180ยฐ.
C) 180ยฐ to 270ยฐ.
D) 270ยฐ to 360ยฐ.
E) It cannot be determined without additional information.
Answer: B
19) Components: If a vector A has components Ax < 0, and Ay 0, and Ay < 0, then the angle that this vector
makes with the positive x-axis must be in the range
A) 0ยฐ to 90ยฐ.
B) 90ยฐ to 180ยฐ.
C) 180ยฐ to 270ยฐ.
D) 270ยฐ to 360ยฐ.
E) It cannot be determined without additional information.
Answer: D
21) Components: The eastward component of vector A is equal to the westward component of vector B
and their northward components are equal. Which one of the following statements must be correct
for these two vectors?
A) The angle between vector A and vector B must be 90ยฐ.
B) Vector A is parallel to vector B .
C) The magnitude of vector A must be equal to the magnitude of vector B .
D) Vector A is antiparallel (in the opposite direction) to vector B .
E) Vector A must be perpendicular to vector B .
Answer: C
22) Components: Vector A is along the +x-axis and vector B is along the +y-axis. Which one of the
following statements is correct with respect to these vectors?
A) The y component of vector A is equal to the y component of vector B .
B) The x component of vector A is equal to the x component of vector B .
C) The x component of vector A is equal to the y component of vector B .
D) The y component of vector A is equal to the x component of vector B .
Answer: D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
23) Components: A velocity vector has components 36 m/s westward and 22 m/s northward. What are
the magnitude and direction of this vector?
Answer: 42 m/s at 31ยฐ north of west
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
24) Components: The x component of vector A is 8.7 units, and its y component is -6.5 units. The
magnitude of A is closest to
A) 9.9 units.
B) 12 units.
C) 8.9 units.
Answer: E
5
D) 7.9 units.
E) 11 units.
25) Components: When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity
vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal?
A) 75ยฐ
B) 33ยฐ
C) 57ยฐ
D) 15ยฐ
Answer: A
26) Components: When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was
5.1 m/s. What was the vertical component of Jeff's velocity?
A) 3.4 m/s
B) 4.8 m/s
C) 4.3 m/s
D) 3.8 m/s
Answer: B
27) Components: The x component of vector A is 5.3 units, and its y component is -2.3 units. The angle
that vector A makes with the +x-axis is closest to
A) 250ยฐ.
B) 340ยฐ.
C) 110ยฐ.
D) 23ยฐ.
E) 160ยฐ.
Answer: B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) Components: A vector in the xy-plane has an x component of -7.50 units. What must be the y
component of this vector so that its magnitude is 10.0 units. (Note: There are two possible answers.)
Answer: +6.6 units and -6.6 units
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
29) Components: A displacement vector is 34.0 m in length and is directed 60.0ยฐ east of north. Selecting from the
choices in the table below, what are the components of this vector?
choice
1
2
3
4
5
Northward
component
29.4 m
18.2 m
22.4 m
17.0 m
25.2 m
A) choice 1
Eastward
component
17.0 m
28.1 m
11.5 m
29.4 m
18.2 m
B) choice 2
C) choice 3
D) choice 4
E) choice 5
Answer: D
30) Components: A player throws a football 50.0 m at 61.0ยฐ north of west. What is the westward
component of the displacement of the football?
A) 55.0 m
B) 64.7m
C) 24.2 m
Answer: C
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D) 74.0 m
E) 0.00 m
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
31) Components: A vector A has components Ax = 12.0 m and Ay = 5.00 m.
(a) What is the angle that vector A makes with the +x-axis?
(b) What is the magnitude of vector A ?
Answer: (a) 22.6ยฐ (b) 13.0 m
32) Components: The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively.
(a) What is the magnitude of this vector?
(b) What angle does this vector make with the positive +y-axis.
Answer: (a) 5.00 m (b) 53.1ยฐ
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
33) Components: A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0ยฐ above the
horizontal. What is the horizontal component of the boy's velocity?
A) 8.45 m/s
B) 18.1 m/s
C) 9.33 m/s
D) 12.6 m/s
E) 15.6 m/s
Answer: B
34) Components: The magnitude of A is 5.5 m, and this vector lies in the second quadrant and makes
an angle of 34 ยฐ with the +y-axis. The components of A are closest to:
A) Ax = -4.6 m, Ay = -3.1 m.
B) Ax = -3.1 m, Ay = 4.6 m.
C) Ax = -4.6 m, Ay = 3.1 m.
D) Ax = 4.6 m, A y = -3.1 m.
E) Ax = 3.1 m, A y = -4.6 m.
Answer: B
35) Components: The components of vectors B and C are given as follows:
Bx = -9.2 C x = -4.5
By = -6.1 C y = 4.3
The angle (less than 180ยฐ) between vectors B and C is closest to
A) 10ยฐ.
B) 77ยฐ.
C) 84ยฐ.
D) 103ยฐ.
E) 170ยฐ.
Answer: B
36) Addition by Components: A car travels 20 km west and then 20 km south. Use components to find
the magnitude of its displacement vector?
A) 20 km
B) 40 km
C) 0 km
Answer: D
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D) 28 km
37) Addition by Components: You walk 33 m to the north, then turn 60ยฐ to your right and walk another
45 m. Use components to find how far you end up from your starting point.
A) 35 m
B) 75 m
C) 39 m
D) 68 m
Answer: D
38) Addition by Components: You walk 53 m to the north, then you turn 60ยฐ to your right and walk
another 45 m. Use components to determine the direction of your displacement vector. Express your
answer as an angle relative to east.
A) 69ยฐ N of E
B) 50ยฐ N of E
C) 63ยฐ N of E
D) 57ยฐ N of E
Answer: C
39) Addition by Components: The components of vectors A and B are given as follows:
Ax = 7.6 Bx = -5.1
Ay = -9.2 By = -6.8
What is the magnitude of the vector difference B – A ?
A) 170
B) 3.4
C) 16
D) 3.5
E) 13
Answer: E
40) Addition by Components: If vector A has components A x = -3.0 lb and A y = -4.0 lb, and vector B
has components B x = 3.0 lb and By = -8.0 lb, what is the magnitude of vector C = A – B ?
A) 16 lb
B) 7.2 lb
C) 140 lb
D) 13 lb
Answer: B
41) Addition by Components: Vector A has magnitude 2 units and is directed to the north. Vector B
has magnitude 5 units and is directed to the south. Calculate the magnitude and direction of A – B .
A) 7 units, north
B) 7 units, south
C) 3 units, south
D) 3 units, north
Answer: A
42) Addition by Components: Two perpendicular vectors, A and B , are added together giving vector
C . If the magnitudes of both vectors A and B are doubled without changing their directions, the
magnitude of vector C will
A) increase by a factor of 4.
B) increase by a factor of 8.
C) increase by a factor of 2 .
D) increase by a factor of 2.
E) not change.
Answer: D
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
43) Addition by Components: Three ropes are tied in a knot as shown in the figure. One student pulls on
rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How
hard and in what direction must you pull on rope C to balance the first two pulls? Give the
direction by specifying the angle (clockwise or counterclockwise) of the pull with the direction of
rope A.
Answer: 6.6 lb at 68ยฐ clockwise from rope A
44) Addition by Components: The figure shows two vectors B and C , along with their magnitudes and
directions. The vector D is given by D = B – C .
(a) What is the magnitude of vector D ?
(b) What angle does vector D make with the +x-axis?
Answer: (a) 6.6 (b) 170ยฐ
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45) Addition by 1. Components: Displacement vector A is 5.5 cm long and points along the +x-axis.
Displacement vector B is 7.5 cm long and points at +30ยฐ to the -x-axis.
(a) Determine the x and y components of vector A .
(b) Determine the x and y components of vector B .
(c) Determine the x and y components of the resultant of these two vectors.
(d) Determine the magnitude and direction of the resultant of these two vectors.
Answer: (a) A x = 5.5 cm, A y = 0 cm (b) B x = -6.5 cm, B y = 3.8 cm
(c) R x = -1.0 cm, Ry = 3.8 cm (d) 3.9 cm at 75ยฐ above the -x axis
46) Addition by 1. Components: Displacement vector A is 75 cm long and points at 30ยฐ above the
+x-axis. Displacement vector B is 25 cm long and points along the -x-axis. Displacement vector C
is 40 cm long and points at 45ยฐ below the -x-axis.
(a) Determine the x and y components of vector A .
(b) Determine the x and y components of vector B .
(c) Determine the x and y components of vector C .
(d) Determine the x and y components of the resultant of these three vectors.
(e) Determine the magnitude and direction of the resultant of these three vectors.
Answer: (a) A x = 65 cm, A y = 38 cm (b) B x = -25 cm, B y = 0 cm
(c) C x = -28 cm, C y = -28 cm (d) Rx = 12 cm, Ry = 9 cm
(e) 15 cm at 38ยฐ above the +x-axis
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
47) Addition by 1. Components: Vector M = 4.00 m points eastward and vector N = 3.00 m points
southward. The resultant vector M + N is given by
A) 5.00 m at an angle of 18.4ยฐ south of east.
B) 5.00 m at an angle of 71.6ยฐ south of east.
C) 5.00 m at an angle of 53.1ยฐ south of east.
D) 5.00 m at an angle of 36.9ยฐ south of east.
E) 5.00 m at an angle of 26.6ยฐ south of east.
Answer: D
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48) Addition by 1. Components: Vector A has a magnitude of 6.0 m and points 30ยฐ north of east.
Vector B has a magnitude of 4.0 m and points 30ยฐ east of north. The resultant vector A + B is
given by
A) 2.0 m at an angle of 42ยฐ north of east.
B) 9.7 m at an angle of 42ยฐ north of east.
C) 0.70 m at an angle of 42ยฐ north of east.
D) 14 m at an angle of 42ยฐ north of east.
E) 1.1 m at an angle of 42ยฐ north of east.
Answer: B
49) Addition by 1. Components: Vector A has a magnitude of 6.0 m and points 30ยฐ north of east.
Vector B has a magnitude of 4.0 m and points 30ยฐ west of north. The resultant vector A + B is
given by
A) 9.8 m at an angle of 26ยฐ north of east.
B) 7.2 m at an angle of 26ยฐ east of north.
C) 3.3 m at an angle of 64ยฐ east of north.
D) 3.3 m at an angle of 26ยฐ north of east.
E) 9.8 m at an angle of 64ยฐ east of north.
Answer: B
50) Addition by 1. Components: Vector A has a magnitude of 6.0 m and points 30ยฐ north of east.
Vector B has a magnitude of 4.0 m and points 30ยฐ west of south. The resultant vector A + B is
given by
A) 3.2 m at an angle of 8.3ยฐ east of south.
B) 2.7 m at an angle of 8.3ยฐ east of south.
C) 2.3 m at an angle of 8.3ยฐ south of east.
D) 2.7 m at an angle of 8.3ยฐ south of east.
E) 3.2 m at an angle of 8.3ยฐ south of east.
Answer: E
51) Addition by 1. Components: Vector A has a magnitude of 6.0 m and points 30ยฐ south of east.
Vector B has a magnitude of 4.0 m and points 30ยฐ west of south. The resultant vector A + B is
given by
A) 9.8 m at an angle of 64ยฐ south of east.
B) 3.3 m at an angle of 64ยฐ south of east.
C) 3.3 m at an angle of 26ยฐ south of east.
D) 7.2 m at an angle of 64ยฐ south of east.
E) 9.8 m at an angle of 26ยฐ south of east.
Answer: D
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52) Addition by 1. Components: Vector A has a magnitude of 4.0 m and points 30ยฐ south of east. Vector
B has a magnitude of 2.0 m and points 30ยฐ north of west. The resultant vector A + B is given by
A) 1.0 m at an angle 30ยฐ east of south.
B) 2.0 m at an angle 60ยฐ south of east.
C) 10.0 m at an angle 60ยฐ east of south.
D) 10.0 m at an angle 30ยฐ south of east.
E) 2.0 m at an angle 30ยฐ south of east.
Answer: E
53) Addition by 1. Components: Vector A has a magnitude of 7.0 m and points 30ยฐ east of north.
Vector B has a magnitude of 5.0 m and points 30ยฐ west of south. The resultant vector A + B is
given by
A) 10.0 m at an angle 60ยฐ north of east.
B) 1.0 m at an angle 60ยฐ east of north
C) 10.0 m at an angle 30ยฐ east of north.
D) 2.0 m at an angle 30ยฐ north of east.
E) 2.0 m at an angle 60ยฐ north of east.
Answer: E
54) Addition by 1. Components: Vector A has a magnitude of 6.0 m and points 30ยฐ east of south.
Vector B has a magnitude of 4.0 m and points 30ยฐ west of north. The resultant vector A + B is
given by
A) 2.0 m at an angle of 30ยฐ north of west.
B) 1.0 m at an angle of 60ยฐ north of west.
C) 2.0 m at an angle of 30ยฐ east of south.
D) 10.0 m at an angle of 60ยฐ north of west.
E) 10.0 m at an angle of 60ยฐ east of south.
Answer: C
55) Addition by 1. Components: Vector A has a magnitude of 8.0 m and points east, vector B has a
magnitude of 6.0 m and points north, and vector C has a magnitude of 5.0 m and points west. The
resultant vector A + B + C is given by
A) 6.7 m at an angle 63ยฐ north of east.
B) 2.0 m at an angle 63ยฐ north of east.
C) 2.0 m at an angle 63ยฐ east of north.
D) 3.8 m at an angle 67ยฐ north of east
E) 6.7 m at an angle 63ยฐ east of north.
Answer: A
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56) Addition by 1. Components: The figure shows three vectors and their magnitudes and relative
directions. The magnitude of the resultant of the three vectors is closest to
A) 7.0.
B) 16.
C) 13.
D) 10.
E) 19.
Answer: C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
57) Addition by 1. Components: Find the magnitude and direction of the resultant of the three force
vectors, A , B , and C , shown in the figure. These vectors have the following magnitudes: A = 5.0
lb, B = 7.9 lb, and C = 8.0 lb. Express the direction of the resultant by specifying the angle it makes
with the +x-axis, with counterclockwise angles taken to be positive.
Answer: 1.6 lb, 312ยฐ
58) Addition by 1. Components: Two boys, Joe and Sam, who are searching for buried treasure start
underneath the same tree. Joe walks 12 m east and then 12 m north, while Sam walks 15 m west and
then 10 m south. Both boys then stop. Find the magnitude and direction of the vector from Sam to
Joe. Express the direction of this vector by specifying the angle it makes with the west-to-east
direction.
Answer: 35 m at 39ยฐ north of east
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
59) Addition by 1. Components: An airplane undergoes the following displacements, all at the same
altitude: First, it flies 59.0 km in a direction 30.0ยฐ east of north. Next, it flies 58.0 km due south.
Finally, it flies 100 km 30.0ยฐ north of west. Use components to determine how far the airplane ends
up from its starting point.
A) 73.0 km
B) 71.5 km
C) 70.1 km
D) 74.4 km
E) 68.7 km
Answer: B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
60) Addition by 1. Components: Two forces are acting on an object as shown in the figure. Assume that
all the quantities shown are accurate to three significant figures.
(a) What is the magnitude of the resultant force on the object?
(b) What is the direction of the resultant force?
Answer: (a) 185 N (b) 77.8ยฐ above the +x-axis
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
61) Addition by 1. Components: Three forces, F 1, F 2, and F 3, each of magnitude 70 N, all act on an
object as shown in the figure. The magnitude of the resultant force acting on the object is
A) 70 N.
B) 140 N.
C) 210 N.
Answer: D
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D) 0 N.
E) 35 N.
62) Addition by 1. Components: Three forces, F 1, F 2, and F 3, all act on an object, as shown in the
figure. The magnitudes of the forces are: F1 = 80.0 N, F 2 = 60.0 N, and F3 = 40.0 N. The resultant
force acting on the object is given by
A) 60.0 N at an angle of 90.0ยฐ with respect to +x-axis.
B) 35.5 N at an angle of 34.3ยฐ with respect to +x-axis.
C) 20.0 N at an angle of 34.3ยฐ with respect to +x-axis.
D) 40.0 N at an angle of 60.0ยฐ with respect to +x-axis.
E) 180 N at an angle of 60.0ยฐ with respect to +x-axis.
Answer: B
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63) Addition by 1. Components: Four vectors, A , B , C , and D , are shown in the figure. The sum of
these four vectors is a vector having magnitude and direction
A) 4.0 cm, along +y-axis.
B) 4.0 cm, 45ยฐ above +x-axis.
C) 4.0 cm, along +x-axis.
D) 4.0 cm, along -y-axis.
E) 4.0 cm, along -x-axis.
Answer: D
64) Addition by 1. Components: Vector A has a magnitude of 8.0 m and points 30ยฐ north of east; vector
B has a magnitude of 6.0 m and points 30ยฐ west of north; and vector C has a magnitude of 5.0 m
and points 30ยฐ west of south. The resultant vector A + B + C is given by
A) 5.1 m at an angle 74ยฐ north of east.
B) 4.8 m at an angle 74ยฐ east of north.
C) 5.9 m at an angle 74ยฐ north of east.
D) 2.1 m at an angle 66ยฐ east of north.
E) 2.7 m at an angle 74ยฐ north of east.
Answer: A
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
65) Addition by 1. Components: The figure shows three vectors, A , B , and C , having magnitudes 7.0
cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three
vectors.
Answer: -11 cm (x component), -4.5 cm (y component)
66) Addition by 1. Components: The figure shows four vectors, A , B , C , and D , having magnitudes
10.0 m, 8.00 m, 6.00 m, and 2.00 m, respectively. Find the magnitude of the sum of these four
vectors.
Answer: 14.4 m
18
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
67) Addition by 1. Components: The figure shows four vectors, A , B , C , and D , having magnitudes
12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is
A) 19.5 m at an angle 12.3ยฐ with respect to +x-axis.
B) 8.20 m at an angle 77.8ยฐ with respect to +x-axis.
C) 16.4 m at an angle 77.8ยฐ with respect to +x-axis.
D) 16.4 m at an angle 12.3ยฐ with respect to +x-axis.
E) 19.5 m at an angle 77.8ยฐ with respect to +x-axis.
Answer: C
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
68) Addition by 1. Components: The figure shows four vectors, A , B , C , and D . Vectors A and B
each have a magnitude of 7.0 cm, and vectors C and D each have a magnitude of 4.0 cm. Find the
x and y components of the sum of these four vectors.
Answer: 0.00 cm (x component), 4.2 cm (y component)
69) Addition by 1. Components: The figure shows four vectors, A , B , C , and D . Vectors A and B
both have a magnitude of 7.0 cm, and vectors C and D both have a magnitude of 4.0 cm. Find the
magnitude and direction of the sum of these four vectors.
Answer: 4.2 cm along the +y-axis
20
70) Addition by 1. Components: The figure shows three vectors, A , B , and C , along with their
magnitudes. Determine the magnitude and direction of the vector given by A – B – C .
Answer: 85 m at 5.4ยฐ above the +x-axis
71) Addition by 1. Components: The figure shows three vectors, A , B , and C , along with their
magnitudes. Determine the magnitude and direction of the vector given by A + B – C .
Answer: 100 m at 31ยฐ above the +x-axis
21
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
72) Addition by 1. Components: Three vectors, S , T , and U , have the components shown in the table.
What is the magnitude of the resultant of these three vectors?
x component y component
S
3.50 m
-4.50 m
T
2.00 m
0.00 m
U
-5.50 m
2.50 m
A) 11.1 m
B) 13.0 m
C) 5.50 m
D) 2.00 m
E) 7.00 m
Answer: D
73) Addition by 1. Components: Three vectors, S , T , and U , have the components shown in the table.
What angle does the resultant of these three vectors make with the +x-axis?
x component y component
S
-3.5 m
4.5 m
T
0.00 m
-6.5 m
U
5.5 m
-2.5 m
A) 24ยฐ above the +x-axis
B) 24ยฐ below the +x-axis
C) 66ยฐ below the +x-axis
D) 66ยฐ above the +x-axis
Answer: C
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