Halliday/Resnick/Walker%20Fundamentals%20of%20Physics

1
Halliday/Resnick/WalkerFundamentals of Physics

• Classroom Response System Questions

Chapter 3 Vectors
Interactive Lecture Questions
2
3.2.1. Which one of the following statements is
true concerning scalar quantities? a) Scalar
quantities must be represented by base units. b)
Scalar quantities have both magnitude and
direction. c) Scalar quantities can be added to
vector quantities using rules of
trigonometry. d) Scalar quantities can be added
to other scalar quantities using rules of
trigonometry. e) Scalar quantities can be added
to other scalar quantities using rules of
ordinary addition.
3
3.2.1. Which one of the following statements is
true concerning scalar quantities? a) Scalar
quantities must be represented by base units. b)
Scalar quantities have both magnitude and
direction. c) Scalar quantities can be added to
vector quantities using rules of
trigonometry. d) Scalar quantities can be added
to other scalar quantities using rules of
trigonometry. e) Scalar quantities can be added
to other scalar quantities using rules of
ordinary addition.
4
3.2.2. Which one of the following situations
involves a vector? a) The submarine followed
the coastline for 35 kilometers. b) The air
temperature in Northern Minnesota dropped to ?4
?C. c) The Hubble Telescope orbits 598 km above
the surface of the earth. d) The baseball flew
into the dirt near home plate at 44 m/s. e) The
flock of Canadian Geese was spotted flying due
south at 5 m/s.
5
3.2.2. Which one of the following situations
involves a vector? a) The submarine followed
the coastline for 35 kilometers. b) The air
temperature in Northern Minnesota dropped to ?4
?C. c) The Hubble Telescope orbits 598 km above
the surface of the earth. d) The baseball flew
into the dirt near home plate at 44 m/s. e) The
flock of Canadian Geese was spotted flying due
south at 5 m/s.
6
3.3.1. Which expression is false concerning the
vectors shown in the sketch? a) b) c) d)
C lt A B e) A2 B2 C2
7
3.3.1. Which expression is false concerning the
vectors shown in the sketch? a) b) c) d)
C lt A B e) A2 B2 C2
8
3.3.2. Three vectors , , and add
together to yield zero 0. The
vectors and point in opposite directions
and their magnitudes are related by the
expression A 2C. Which one of the following
conclusions is correct? a) and point in
the same direction, but has twice the
magnitude of . b) and
have equal magnitudes and point in opposite
directions. c) and point in the same
direction, but has twice the magnitude of
. d) and have equal magnitudes and
point in opposite directions. e) and
have equal magnitudes and point in the same
direction.
9
3.3.2. Three vectors , , and add
together to yield zero 0. The
vectors and point in opposite directions
and their magnitudes are related by the
expression A 2C. Which one of the following
conclusions is correct? a) and point in
the same direction, but has twice the
magnitude of . b) and
have equal magnitudes and point in opposite
directions. c) and point in the same
direction, but has twice the magnitude of
. d) and have equal magnitudes and
point in opposite directions. e) and
have equal magnitudes and point in the same
direction.
10
3.3.3. Two vectors and are added together
to form a vector The relationship between the
magnitudes of the vectors is given by a b c.
Which one of the following statements concerning
these vectors is true? a) and must point
in the same direction. b) and must be
displacements. c) and must be at right
angles to each other. d) and must point
in opposite directions. e) and must have
equal lengths.
11
3.3.3. Two vectors and are added together
to form a vector The relationship between the
magnitudes of the vectors is given by a b c.
Which one of the following statements concerning
these vectors is true? a) and must point
in the same direction. b) and must be
displacements. c) and must be at right
angles to each other. d) and must point
in opposite directions. e) and must have
equal lengths.
12
3.3.4. Two vectors and are added together
to form a vector The relationship between the
magnitudes of the vectors is given by a2 b2
c2. Which one of the following statements
concerning these vectors is true? a) and
must be parallel. b) and could have any
orientation relative to each other. c) and
must be at right angles to each other. d)
and must point in opposite directions. e)
and must have equal lengths.
13
3.3.4. Two vectors and are added together
to form a vector The relationship between the
magnitudes of the vectors is given by a2 b2
c2. Which one of the following statements
concerning these vectors is true? a) and
must be parallel. b) and could have any
orientation relative to each other. c) and
must be at right angles to each other. d)
and must point in opposite directions. e)
and must have equal lengths.
14
3.3.5. What is the minimum number of vectors with
unequal magnitudes whose vector sum can be
zero? a) 2 b) 3 c) 4 d) 5 e) 6
15
3.3.5. What is the minimum number of vectors with
unequal magnitudes whose vector sum can be
zero? a) 2 b) 3 c) 4 d) 5 e) 6
16
3.3.6. What is the minimum number of vectors with
equal magnitudes whose vector sum can be
zero? a) 2 b) 3 c) 4 d) 5 e) 6
17
3.3.6. What is the minimum number of vectors with
equal magnitudes whose vector sum can be
zero? a) 2 b) 3 c) 4 d) 5 e) 6
18
3.3.7. A physics student adds two displacement
vectors with magnitudes of 8.0 km and 6.0 km.
Which one of the following statements is true
concerning the magnitude of the resultant
displacement? a) The magnitude must be 14.0
km. b) The magnitude must be 10.0 km. c) The
magnitude could be equal to zero kilometers,
depending on how the vectors are oriented. d)
The magnitude could have any value between 2.0 km
and 14.0 km, depending on how the vectors are
oriented. e) No conclusion can be reached
without knowing the directions of the vectors.
19
3.3.7. A physics student adds two displacement
vectors with magnitudes of 8.0 km and 6.0 km.
Which one of the following statements is true
concerning the magnitude of the resultant
displacement? a) The magnitude must be 14.0
km. b) The magnitude must be 10.0 km. c) The
magnitude could be equal to zero kilometers,
depending on how the vectors are oriented. d)
The magnitude could have any value between 2.0 km
and 14.0 km, depending on how the vectors are
oriented. e) No conclusion can be reached
without knowing the directions of the vectors.
20
3.3.8. Two displacement vectors of magnitudes 21
cm and 79 cm are added. Which one of the
following is the only possible choice for the
magnitude of the resultant? a) 0 cm b) 28
cm c) 37 cm d) 82 cm e) 114 cm
21
3.3.8. Two displacement vectors of magnitudes 21
cm and 79 cm are added. Which one of the
following is the only possible choice for the
magnitude of the resultant? a) 0 cm b) 28
cm c) 37 cm d) 82 cm e) 114 cm
22
3.4.1. During the execution of a play, a football
player carries the ball for a distance of 33 m in
the direction 76 north of east. To determine
the number of meters gained on the play, find the
northward component of the balls
displacement. a) 8.0 m b) 16 m c) 24 m d)
28 m e) 32 m
23
3.4.1. During the execution of a play, a football
player carries the ball for a distance of 33 m in
the direction 76 north of east. To determine
the number of meters gained on the play, find the
northward component of the balls
displacement. a) 8.0 m b) 16 m c) 24 m d)
28 m e) 32 m
24
3.4.2. The city of Denver is located
approximately one mile (1.61 km) above sea level.
Assume you are standing on a beach in Los
Angeles, California, at sea level estimate the
angle of the resultant vector with respect to the
horizontal axis between your location in
California and Denver. a) between 1? and 2? b)
between 0.5? and 0.9? c) between 0.11? and
0.45? d) between 0.06? and 0.10? e) less than
0.05?
25
3.4.2. The city of Denver is located
approximately one mile (1.61 km) above sea level.
Assume you are standing on a beach in Los
Angeles, California, at sea level estimate the
angle of the resultant vector with respect to the
horizontal axis between your location in
California and Denver. a) between 1? and 2? b)
between 0.5? and 0.9? c) between 0.11? and
0.45? d) between 0.06? and 0.10? e) less than
0.05?
26
3.4.3. Determine the angle ? in the right
triangle shown. a) 54.5? b) 62.0? c)
35.5? d) 28.0? e) 41.3?
27
3.4.3. Determine the angle ? in the right
triangle shown. a) 54.5? b) 62.0? c)
35.5? d) 28.0? e) 41.3?
28
3.4.4. Determine the length of the side of the
right triangle labeled x. a) 2.22 m b)
1.73 m c) 1.80 m d) 2.14 m e) 1.95 m
29
3.4.4. Determine the length of the side of the
right triangle labeled x. a) 2.22 m b)
1.73 m c) 1.80 m d) 2.14 m e) 1.95 m
30
3.4.5. Determine the length of the side of the
right triangle labeled x. a) 0.79 km b)
0.93 km c) 1.51 km d) 1.77 km e) 2.83 km
31
3.4.5. Determine the length of the side of the
right triangle labeled x. a) 0.79 km b)
0.93 km c) 1.51 km d) 1.77 km e) 2.83 km
32
3.4.6. Consider the two vectors shown. Complete
the following statement The component of vector
along vector is a) equal to zero. b)
smaller than B. c) equal to B. d) larger
than B. e) perpendicular to vector .
33
3.4.6. Consider the two vectors shown. Complete
the following statement The component of vector
along vector is a) equal to zero. b)
smaller than B. c) equal to B. d) larger
than B. e) perpendicular to vector .
34
3.4.7. In a two-dimensional coordinate system,
the angle between the positive x axis and vector
is ?. Which one of the following choices is
the expression to determine the x-component of
? a) A sin ? b) A tan ? c) A cos ? d) A
cos?1 ? e) A/sin ?
35
3.4.7. In a two-dimensional coordinate system,
the angle between the positive x axis and vector
is ?. Which one of the following choices is
the expression to determine the x-component of
? a) A sin ? b) A tan ? c) A cos ? d) A
cos?1 ? e) A/sin ?
36
3.4.8. In a two-dimensional coordinate system,
the angle between the positive y axis and vector
is ?. Which one of the following choices is
the expression to determine the x-component of
? a) A sin ? b) A tan ? c) A cos ? d) A
cos?1 ? e) A/sin ?
37
3.4.8. In a two-dimensional coordinate system,
the angle between the positive y axis and vector
is ?. Which one of the following choices is
the expression to determine the x-component of
? a) A sin ? b) A tan ? c) A cos ? d) A
cos?1 ? e) A/sin ?
38
3.4.9. An escaped convict runs 1.70 km due east
of the prison. He then runs due north to a
friends house. If the magnitude of the
convicts total displacement vector is 2.50 km,
what is the direction of his total displacement
vector with respect to due east? a) 43? south
of east b) 47? north of east c) 56? north of
east d) 34? south of east e) 34? north of east
39
3.4.9. An escaped convict runs 1.70 km due east
of the prison. He then runs due north to a
friends house. If the magnitude of the
convicts total displacement vector is 2.50 km,
what is the direction of his total displacement
vector with respect to due east? a) 43? south
of east b) 47? north of east c) 56? north of
east d) 34? south of east e) 34? north of east
40
3.4.10. A displacement vector is 23 km in length
and directed 65 south of east. What are the
components of this vector? Eastward
Component Southward Component a) 21 km 9.7
km b) 23 km 23 km c) 23 km 0 km d) 9.7
km 21 km e) 0 km 23 km
41
3.4.10. A displacement vector is 23 km in length
and directed 65 south of east. What are the
components of this vector? Eastward
Component Southward Component a) 21 km 9.7
km b) 23 km 23 km c) 23 km 0 km d) 9.7
km 21 km e) 0 km 23 km
42
3.6.1. , , and, are vectors.
Vectors and when added together equal the
vector . Vector has a magnitude of 88
units and it is directed at an angle of 44?
relative to the x axis as shown. Find the scalar
components of vectors and
. Bx By Cx Cy a) 63 0 0 61 b) 0 61 63 0 c)
63 0 61 0 d) 0 63 0 61 e) 61 0 63 0
43
3.6.1. , , and, are vectors.
Vectors and when added together equal the
vector . Vector has a magnitude of 88
units and it is directed at an angle of 44?
relative to the x axis as shown. Find the scalar
components of vectors and
. Bx By Cx Cy a) 63 0 0 61 b) 0 61 63 0 c)
63 0 61 0 d) 0 63 0 61 e) 61 0 63 0
44
3.8.1. Consider the various vectors given in the
choices below. The cross product of which pair
of vectors is equal to zero?
45
3.8.1. Consider the various vectors given in the
choices below. The cross product of which pair
of vectors is equal to zero?
46
3.8.2. What is the scalar product, ,
if a) zero b) ?0.9 c) d) 3.1 e)
47
3.8.2. What is the scalar product, ,
if a) zero b) ?0.9 c) d) 3.1 e)
48
3.8.3. What is the vector product, ,
if a) zero b) c) d) e) 8.3
49
3.8.3. What is the vector product, ,
if a) zero b) c) d) e) 8.3
50
3.8.4. The scalar product of two vectors,
, can be determined in a variety of ways.
Which one of the following choices is false? a)
AB cos ?, where ? is the smallest
angle between the two vectors. b) The scalar
product is the product of B and the component of
in the direction of . c) The scalar
product of these two vectors could be equal to
zero. d) The scalar product is the product of A
and the component of in the direction of
. e) The scalar product is equal to the product
of the magnitudes of the two vectors and the sine
of the smallest angle between the two vectors.
51
3.8.4. The scalar product of two vectors,
, can be determined in a variety of ways.
Which one of the following choices is false? a)
AB cos ?, where ? is the smallest
angle between the two vectors. b) The scalar
product is the product of B and the component of
in the direction of . c) The scalar
product of these two vectors could be equal to
zero. d) The scalar product is the product of A
and the component of in the direction of
. e) The scalar product is equal to the product
of the magnitudes of the two vectors and the sine
of the smallest angle between the two vectors.
52
3.8.5. The vector product of two vectors is equal
to zero, but the magnitudes of the two vectors
are not equal to zero. Which one of the
following statements is true? a) Based on the
definition of the vector product, this situation
can never occur. b) The two vectors must be
perpendicular to each other. c) The two vectors
must be parallel to each other. d) The two
vectors must be unit vectors. e) This can only
be true if the scalar product is also equal to
zero.
53
3.8.5. The vector product of two vectors is equal
to zero, but the magnitudes of the two vectors
are not equal to zero. Which one of the
following statements is true? a) Based on the
definition of the vector product, this situation
can never occur. b) The two vectors must be
perpendicular to each other. c) The two vectors
must be parallel to each other. d) The two
vectors must be unit vectors. e) This can only
be true if the scalar product is also equal to
zero.
54
3.8.6. Which of the following vector operations
produces a vector as the result if the magnitudes
of all of the vectors are not equal to
zero? a) b) c) d) e)
55
3.8.6. Which of the following vector operations
produces a vector as the result if the magnitudes
of all of the vectors are not equal to
zero? a) b) c) d) e)