Quiz 3: Vectors and Coordinate Systems
Physics & Astronomy
Q 1Q 1
Which of the following is an accurate statement?
A) The magnitude of a vector can be zero even though one of its components is not zero.
B) It is possible to add a scalar quantity to a vector.
C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector.
E) The magnitude of a vector is independent of the coordinate system used.
Free
Multiple Choice
E
Q 2Q 2
If

= 0, then the vectors
and
have equal magnitudes and are directed in the opposite directions from each other.
Free
True False
False
Q 3Q 3
Under what condition is  
 = A + B?
A) The magnitude of vector is zero.
B) Vectors and are in opposite directions.
C) Vectors and are in the same direction.
D) Vectors and are in perpendicular directions.
E) The statement is never true.
Free
Multiple Choice
B
Q 4Q 4
If A > B, under what condition is  
 = A  B?
A) The statement is never true.
B) Vectors and are in opposite directions.
C) Vectors and are in the same direction.
D) Vectors and re in perpendicular directions.
E) The statement is always true.
Free
Multiple Choice
Free
Essay
Free
True False
Q 7Q 7
If the magnitude of vector
is less than the magnitude of vector
, then the x component of
is less than the x component of
.
Free
True False
Q 8Q 8
If the eastward component of vector is equal to the westward component of vector
And their northward components are equal. Which one of the following statements about these two vectors is correct?
A) Vector is parallel to vector .
B) Vectors and point in opposite directions.
C) Vector is perpendicular to vector .
D) The magnitude of vector is equal to the magnitude of vector .
E) The magnitude of vector is twice the magnitude of vector .
Free
Multiple Choice
Free
True False
Q 10Q 10
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
Free
Multiple Choice
Q 11Q 11
Vectors and
Are shown in the figure. Vector
Is given by
=

. The magnitude of vector
Is 16.0 units, and the magnitude of vector
Is 7.00 units. What is the magnitude of vector
?
A) 9.00
B) 9.53
C) 15.5
D) 16.2
E) 17.5
Free
Multiple Choice
Q 12Q 12
Vectors and
Are shown in the figure. Vector
Is given by
=

. The magnitude of vector
Is 16.0 units, and the magnitude of vector
Is 7.00 units. What is the angle of vector
, measured counterclockwise from the +xaxis?
A) 16.9°
B) 22.4°
C) 73.1°
D) 287°
E) 292°
Free
Multiple Choice
Q 13Q 13
A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?
A) 8.8 m
B) 8.1 m
C) 66 m
D) 10 m
Free
Multiple Choice
Q 14Q 14
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
Free
Multiple Choice
Q 15Q 15
Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector
.
A) A_{x} = 3.83 and A_{y} = 3.21
B) A_{x} = 3.83 and A_{y} = 3.21
C) A_{x} = 3.21 and A_{y} = 3.83
D) A_{x} = 3.21 and A_{y} = 3.83
E) A_{x} = 4.29 and A_{y} = 2.16
Free
Multiple Choice
Q 16Q 16
The components of vector are
= + 3.90 and
= 4.00. What is the angle measured counterclockwise from the +xaxis to vector
?
A) 314°
B) 134°
C) 224°
D) 136°
E) 46.0°
Free
Multiple Choice
Q 17Q 17
Vector
has a magnitude of 5.5 cm and points along the xaxis. Vector
has a magnitude of 7.5 cm and points at +30° above the negative xaxis.
(a) Determine the x and y components of Vector
.
(b) Determine the x and y components of Vector
(c) Determine x and y components of the sum of these two vectors.
(d) Determine the magnitude and direction of the sum of these two vectors.
Free
Essay
Q 18Q 18
Vector
has a magnitude of 75.0 cm and points at 30° above the positive xaxis. Vector
has a magnitude of 25.0 cm and points along the negative xaxis. Vector
has a magnitude of 40.0 cm and points at 45° below the negative xaxis.
(a) Determine the x and y components of Vector
.
(b) Determine the x and y components of Vector
.
(c) Determine the x and y components of Vector
.
(d) Determine x and y components of the sum of these three vectors.
(e) Determine the magnitude and direction of the sum of these three vectors.
Free
Essay
Q 19Q 19
A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?
A) 8.9 m/s
B) 220 m/s
C) 435 m/s
D) 444 m/s
Free
Multiple Choice
Q 20Q 20
An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?
A) 5.5 m/s
B) 8.7 m/s
C) 12 m/s
D) 15 m/s
Free
Multiple Choice
Q 21Q 21
The components of vector are
= +2.2 and
= 6.9 , and the components of vector
Are given are
= 6.1 and
= 2.2. What is the magnitude of the vector

?
A) 9.5
B) 6.1
C) 9.9
D) 91
E) 0.76
Free
Multiple Choice
Q 22Q 22
The components of vector are
= 3.5 and
= 9.7, and the components of vector
Are
= 6 and
= +8.1. What is the angle (less than 180 degrees) between vectors
And
?
A) 124°
B) 56°
C) 17°
D) 163°
E) 106°
Free
Multiple Choice
Q 23Q 23
An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point.
A) 79 km
B) 81 km
C) 82 km
D) 78 km
E) 76 km
Free
Multiple Choice
Q 24Q 24
In the figure, the magnitude of vector
is 18.0 units, and the magnitude of vector
is 12.0 units. What vector
must be added to the vectors
and
so that the resultant of these three vectors points in the x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector
by giving its magnitude and the angle it makes with the +xaxis taking counterclockwise to be positive.
Free
Short Answer
Q 25Q 25
Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes = 1.0 N,
= 8.0 N and
= 7.0 N, where N is the standard unit of force, what is the component of the net force
_{net} =
_{1 }+
_{2 }+
_{3} parallel to the floor?
A) 2.5 N
B) 5.1 N
C) 6.0 N
D) 7.8 N
Free
Multiple Choice
Q 26Q 26
As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N,
= 60.0 N, and
= 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by
A) 180 N at an angle 60.0° with respect to +xaxis.
B) 60.0 N at an angle 90.0° with respect to +xaxis.
C) 20.0 N at an angle 34.3° with respect to +xaxis.
D) 35.5 N at an angle 34.3° with respect to +xaxis.
E) 40.0 N at an angle 60.0° with respect to +xaxis.
Free
Multiple Choice
Q 27Q 27
A teacher sends her students on a treasure hunt. She gives the following instructions:
1. Walk 300 m north
2. Walk 400 m northwest
3. Walk 700 m eastsoutheast and the treasure is buried there.
As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?
A) 187 m in a direction 67.3° north of east
B) 481 m in a direction 40.9° north of east
C) 399 m in a direction 52.5° north of east
D) 284 m in a direction 28.2° west of north
E) The treasure position cannot be reached in one straight walk.
Free
Multiple Choice
Q 28Q 28
Vector = 3.00
+ 3.00
And vector
= 3.00
+ 4.00
. What is vector
=
+
?
A) 0.00 + 3.00
B) 7.00 + 7.00
C) 3.00 + 7.00
D) 0.00 + 7.00
E) 3.00 3.00
Free
Multiple Choice
Q 29Q 29
Vector = 1.00
+ 2.00
And vector
= 3.00
+ 4.00
. What are the magnitude and direction of vector
=
+
?
A) 7.21 in a direction 33.7° counterclockwise from the positive x axis
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis
Free
Multiple Choice
Q 30Q 30
What is the magnitude of +
+
, where
= 1.00
+ 4.00
 1.00
,
= 3.00
 1.00
 4.00
And
= 1.00
+ 1.00
?
A) 7.07
B) 2.00
C) 10.76
D) 6.78
E) 8.12
Free
Multiple Choice
Q 31Q 31
If = +4
 2
 3
And
= 4
2
 3
, which of the following numbers is closest to the magnitude of

?
A) 8
B) 7
C) 9
D) 10
E) 11
Free
Multiple Choice
Q 32Q 32
Vector = 1.00
+ 2.00
And vector
= 3.00
+ 4.00
. What are the magnitude and direction of vector
= 3.00
+ 2.00
?
A) 3.61 in a direction 56.3° counterclockwise from the positive xaxis
B) 3.61 in a direction 56.3° counterclockwise from the positive xaxis
C) 3.61 in a direction 33.7° counterclockwise from the positive xaxis
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis
E) 6.72 in a direction 34.4° counterclockwise from the positive xaxis
Free
Multiple Choice
Q 33Q 33
Vectors and
Are shown in the figure. What is
?
A) 31.8
B) 32.0  2.00
C) 1028
D) 34.0
E) 2.00  32.0
Free
Multiple Choice