# Physics Lecture 4

B
The main difference between an scalar and a vector quantity is:
A) Magnitude
B) Direction
C) Unit
A
The components of vectors B and C are given as follows:
Bx = -9.2 Cx = -4.5
By = -6.1 Cy = + 4.3
The angle (less than 180 degrees) between vectors B and C , in degrees, is closest to:
A) 77
B) 103
C) 10
D) 170
E) 84
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A
The magnitude of A is 5.5. Vector A lies in the second quadrant and forms an angle of 34 degrees with the y-axis. The components, Ax and Ay, are closest to:
A) Ax = – 3.1, Ay = + 4.6
B) Ax = + 3.1, Ay = – 4.6
C) Ax = + 4.6, Ay = – 3.1
D) Ax = – 4.6, Ay = + 3.1
E) Ax = – 4.6, Ay = – 3.1
D
Vector A has length 4 units and directed to the north. Vector B has length 9 units and is
directed to the south. Calculate the magnitude and direction of A + B .
A) 13 units, south
B) 5 units, north
C) 13 units, north
D) 5 units, south
A
You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?
A) 87 m
B) 50 m
C) 94 m
D) 46 m
A
You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.
A) 63° N of E
B) 50° N of E
C) 57° N of E
D) 69° N of E
A
Vector A points to the north and has length A. Vector B points to the east and has length
B = 2.0 A. Find the magnitude of C = 4 A + B in terms of A.
A) 4.5A
B) 6A
C) 3.6A
D) 3.1A
B
The main difference between an scalar and a vector quantity is:
A) Magnitude
B) Direction
C) Unit
A
Vector A points to the north and has length A. Vector B points to the east and has length
B = 2.5A. Find the direction of C = 7.4 A + B . Express your answer as an angle relative to east.
A) 71° north of east
B) 19° north of east
C) 82° north of east
D) 60° north of east
D
Two vectors A and B are added together to form a vector C . 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) A and B must be displacements.
B) A and B must have equal lengths.
C) A and B must point in opposite directions.
D) A and B must point in the same direction.
E) A and B must be at right angles to each other.
A
Two vectors A and B are added together to form a vector C . The relationship between the magnitudes of the vectors is given by: A2 + B2 = C2. Which statement concerning these vectors is true?
A) A and B must be at right angles to each other.
B) A and B could have any orientation relative to each other.
C) A and B must have equal lengths.
D) A and B must be parallel.
E) A and B could be antiparallel.
B
Three vectors A , B , and C add together to yield zero: A + B + C = 0. The vectors A
and C point in opposite directions and their magnitudes are related by the expression: A = 2C. Which one of the following conclusions is correct?
A) A and B have equal magnitudes and point in opposite directions.
B) B and C have equal magnitudes and point in the same direction.
C) B and C have equal magnitudes and point in opposite directions.
D) A and B point in the same direction, but A has twice the magnitude of B.
E) B and C point in the same direction, but C has twice the magnitude of B.
C
What is the angle between the vectors A and -A when they are drawn from a common origin?
A) 0°
B) 90°
C) 180°
D) 270°
E) 360°
D
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
A
Which expression is false concerning the vectors shown in the sketch?
A) C = A + B
B) C + A = -B
C) A + B + C = 0
D) C < A + B E) A 2 + B 2 = C 2
C
Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:
A = 2.0 km, east; B = 5.2 km, north; C = 4.9 km, west; D = 3.0 km, south What is the resultant displacement R of the members of the bicycle club: R = A + B + C + D?
A) 0.8 km, south
B) 0.4 km, 45° south of east
C) 3.6 km, 37° north of west
D) 4.0 km, east
E) 4.0 km, south
D
A force, F1 , of magnitude 2.0 N and directed due east is exerted on an object. A second
force exerted on the object is F2 = 2.0 N, due north. What is the magnitude and direction of
a third force, F3 , which must be exerted on the object so that the resultant force is zero?
A) 1.4 N, 45° north of east
B) 1.4 N, 45° south of west
C) 2.8 N, 45° north of east
D) 2.8 N, 45° south of west
E) 4.0 N, 45° east of north
C
Three vectors A , B , and C have the following x and y components: Ax = 1 m, Ay = 0 m, Bx = 1 m, By = 1 m, Cx = 0 m, Cy = -1 m
According to the graph, how are A , B , and C combined to result in the vector D ?
A) D = A – B – C
B) D = A – B + C
C) D = A + B – C
D) D = A + B + C
E) D = -A + B + C
D
Which one of the following statements concerning vectors and scalars is false?
A) In calculations, the vector components of a vector may be used in place of the vector itself.
B) It is possible to use vector components that are not perpendicular.
C) A scalar component may be either positive or negative.
D) A vector that is zero may have components other than zero.
E) Two vectors are equal only if they have the same magnitude and direction.
D
Use the component method of vector addition to find the resultant of the following three vectors:
A = 56 km, east B = 11 km, 22° south of east C = 88 km, 44° west of south
A) 81 km, 14° west of south
B) 97 km, 62° south of east
C) 52 km, 66° south of east
D) 68 km, 86° south of east
E) 66 km, 7.1° west of south
C
A vector F1 has a magnitude of 40.0 units and points 35.0° above the positive x axis. A
second vector F2 has a magnitude of 65.0 units and points in the negative x direction. Use
the component method of vector addition to find the magnitude and direction, relative to the positive x axis, of the resultant F = F1 + F2
A) 53.3 units, 141.8° relative to the +x axis
B) 53.3 units, 52.1° relative to the +x axis
C) 39.6 units, 125.4° relative to the +x axis
D) 39.6 units, 54.6° relative to the +x axis
E) 46.2 units, 136.0° relative to the +x axis
C
Two vectors A and B , are added together to form the vector C = A + B . The relationship between the magnitudes of these vectors is given by: Cx = A cos 30° + B and Cy = -A sin 30°. Which statement best describes the orientation of these vectors?
A) A points in the negative x direction while B points in the positive y direction.
B) A points in the negative y direction while B points in the positive x direction.
C) A points 30° below the positive x axis while B points in the positive x direction.
D) A points 30° above the positive x axis while B points in the positive x direction.
E) A points 30° above the negative x axis while B points in the positive x direction.
F
If a vector pointing to the right has a positive magnitude, then one pointing to the left has a negative magnitude.
F
Since vectors always have positive magnitudes, the sum of two vectors must have a magnitude greater than the magnitude of either one of them.
F
The product of a vector by a scalar is a vector having the same direction of the original vector
but a different magnitude.
T
The magnitude of a vector cannot be smaller than the magnitude of any of its components
F
The magnitude of the resultant of two vectors must be greater than or equal to the magnitude
of each of these vectors.
F
The magnitude of the displacement vector from A to B can never be less than the distance
from A to B, but it can be greater than that distance.
F
The magnitude of the displacement vector of an object is equal to the distance that object has
moved.
F
The components of a vector will be the same no matter what coordinate system is used to
express that vector

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