Halliday/Resnick/Walker Fundamentals of Physics Classroom Response System Questions Chapter 3 Vectors Interactive Lecture Questions

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.

3.2.1. 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.

3.2.2. 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.

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.

3.3.1. Which expression is false concerning the vectors shown in the sketch? b) c) d) C < A + B e) A2 + B2 = C2

3.3.1. Which expression is false concerning the vectors shown in the sketch? b) c) d) C < A + B e) A2 + B2 = C2

3. 3. 2. Three vectors , , and add together to yield zero: + + = 0 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.

3. 3. 2. Three vectors , , and add together to yield zero: + + = 0 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.

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.

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.

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.

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.

3.3.5. What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?

3.3.5. What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?

3.3.6. What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?

3.3.6. What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?

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.

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.

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

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

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 ball’s displacement. a) 8.0 m b) 16 m c) 24 m d) 28 m e) 32 m

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 ball’s displacement. a) 8.0 m b) 16 m c) 24 m d) 28 m e) 32 m

3. 4. 2. The city of Denver is located approximately one mile (1 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

3. 4. 2. The city of Denver is located approximately one mile (1 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

3.4.3. Determine the angle  in the right triangle shown. b) 62.0 c) 35.5 d) 28.0 e) 41.3

3.4.3. Determine the angle  in the right triangle shown. b) 62.0 c) 35.5 d) 28.0 e) 41.3

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

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

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

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

3. 4. 6. Consider the two vectors shown 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 .

3. 4. 6. Consider the two vectors shown 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 .

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 

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 

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 

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 

3. 4. 9. An escaped convict runs 1. 70 km due east of the prison 3.4.9. An escaped convict runs 1.70 km due east of the prison. He then runs due north to a friend’s house. If the magnitude of the convict’s 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

3. 4. 9. An escaped convict runs 1. 70 km due east of the prison 3.4.9. An escaped convict runs 1.70 km due east of the prison. He then runs due north to a friend’s house. If the magnitude of the convict’s 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

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

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

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

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

3. 8. 1. Consider the various vectors given in the choices below 3.8.1. Consider the various vectors given in the choices below. The cross product of which pair of vectors is equal to zero?

3. 8. 1. Consider the various vectors given in the choices below 3.8.1. Consider the various vectors given in the choices below. The cross product of which pair of vectors is equal to zero?

3.8.2. What is the scalar product, , if a) zero b) 0.9 c) d) 3.1 e)

3.8.2. What is the scalar product, , if a) zero b) 0.9 c) d) 3.1 e)

3.8.3. What is the vector product, , if a) zero b) c) d) e) 8.3

3.8.3. What is the vector product, , if a) zero b) c) d) e) 8.3

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.

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.

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.

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.

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)

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)