Deck 3: Vectors in Physics

Question 1

You are trying to cross a river that flows toward the south with a strong current.You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point.You should head your motorboat

A)directly toward the west.
B)directly toward the north.
C)in a general southwesterly direction.
D)in a general northwesterly direction.

Answer 1

in a general northwesterly direction.

Question 2

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)10 mm
B)20 mm
C)40 mm
D)80 mm

Answer 2

40 mm

Question 3

If a vector
Has components A_x < 0,and A_y < 0,then the angle that this vector makes with the positive x-axis must be in the range

A)0° to 90°.
B)90° to 180°.
C)180° to 270°.
D)270° to 360°.
E)cannot be determined without additional information

Answer 3

180° to 270°.

Question 4

Vector
Is along the +x-axis and vector
Is along the +y-axis.Which one of the following statements is correct with respect to these vectors?

A)The x component of vector is equal to the x component of vector
.
B)The y component of vector is equal to the y component of vector
.
C)The x component of vector is equal to the y component of vector
.
D)The y component of vector is equal to the x component of vector
.

Question 5

If three vectors add to zero,they must all have equal magnitudes.

Question 6

If a vector's components are all negative,then the magnitude of the vector is negative.

Question 7

If - = 0,then the vectors and have equal magnitudes and are directed in the same direction.

Question 8

The magnitude of a vector an only zero if all of its components are zero.

Question 9

The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is

A)90°.
B)180°.
C)60°.
D)0°.
E)270°.

Question 10

If
+
=
And their magnitudes are given by A + B = C,then the vectors
And
Are oriented

A)perpendicular relative to one other.
B)parallel to each other (in the same direction).
C)antiparallel to each other (in opposite directions).
D)It is impossible to know from the given information.

Question 11

The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is

A)0°.
B)90°.
C)270°.
D)180°.
E)360°.

Question 12

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)is equal to 2.0 m.
B)could be as small as 2.0 m or as large as 12 m.
C)is equal to 12 m.
D)is equal to 8.6 m.

Question 13

Consider two vectors
And
Shown in the figure.The difference
-
Is best illustrated by

A)choice (a).
B)choice (b).
C)choice (c).
D)choice (d).

Question 14

Vectors
And
Obey the equation
+
= 0.These vectors satisfy which one of the following statements?

A)Vectors and
are at right angles to each other.
B)Vectors and
point in the same direction.
C)Vectors and
have the same magnitudes.
D)The magnitude of is the negative of the magnitude of
.

Question 15

If a vector
Has components A_x > 0,and A_y < 0,then the angle that this vector makes with the positive x-axis must be in the range

A)0° to 90°.
B)90° to 180°.
C)180° to 270°.
D)270° to 360°.
E)cannot be determined without additional information

Question 16

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 must be correct for these two vectors?

A)Vector is parallel to vector
.
B)Vector is antiparallel (in the opposite direction)to vector
.
C)Vector must be perpendicular to vector
.
D)The magnitude of vector must be equal to the magnitude of vector
.
E)The angle between vector and vector
must be 90°.

Question 17

The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

Question 18

Consider two vectors
And
Shown in the figure.The difference
-
Is best illustrated by

A)choice (a).
B)choice (b).
C)choice (c).
D)choice (d).

Question 19

If a vector
Has components A_x < 0,and A_y > 0,then the angle that this vector makes with the positive x-axis must be in the range

A)0° to 90°.
B)90° to 180°.
C)180° to 270°.
D)270° to 360°.
E)cannot be determined without additional information

Question 20

The magnitude of a vector can never be less than the magnitude of any of its components.

Question 21

If vector
Has components A_x = -3.0 lb and A_y = -4.0 lb,and vector
Has components B_x = 3.0 lb and B_y = -8.0 lb,what is the magnitude of vector
=
-
?

A)13 lb
B)16 lb
C)140 lb
D)7.2 lb

Question 22

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)4.8 m/s
B)4.3 m/s
C)3.8 m/s
D)3.4 m/s

Question 23

A displacement vector is 34.0 m in length and is directed 60.0° east of north.Selecting from the choices in the table below,what are the components of this vector?

A)choice 1
B)choice 2
C)choice 3
D)choice 4
E)choice 5

Question 24

The components of vectors
And
Are given as follows:
= -9.2
= -4.5
= -6.1
= 4.3
The angle (less than 180°)between vectors
And
Is closest to

A)77°.
B)103°.
C)10°.
D)170°.
E)84°.

Question 25

Vector
Has a magnitude of 6.0 m and points 30° north of east.Vector
Has a magnitude of 4.0 m and points 30° east of north.The resultant vector
+
Is given by

A)0.70 m at an angle of 42° north of east.
B)14 m at an angle of 42° north of east.
C)1.1 m at an angle of 42° north of east.
D)9.7 m at an angle of 42° north of east.
E)2.0 m at an angle of 42° north of east.

Question 26

The x component of vector
Is 5.3 units,and its y component is -2.3 units.The angle that vector
Makes with the +x-axis is closest to

A)340°.
B)160°.
C)250°.
D)110°.
E)23°.

Question 27

Vector
Has magnitude 2 units and is directed to the north.Vector
Has magnitude
And is directed to the south.Calculate the magnitude and direction of

A)7 units,north
B)7 units,south
C)3 units,north
D)3 units,south

Question 28

The x component of vector
Is 8.7 units,and its y component is -6.5 units.The magnitude of
Is closest to

A)9.9 units.
B)7.9 units.
C)8.9 units.
D)11 units.
E)12 units.

Question 29

Two perpendicular vectors,
And
,are added together giving vector
.If the magnitudes of both vectors
And
Are doubled without changing their directions,the magnitude of vector
Will

A)increase by a factor of 8.
B)increase by a factor of 4.
C)increase by a factor of 2.
D)increase by a factor of .
E)not change.

Question 30

Vector
Has a magnitude of 6.0 m and points 30° north of east.Vector
Has a magnitude of 4.0 m and points 30° west of north.The resultant vector
+
Is given by

A)9.8 m at an angle of 64° east of north.
B)9.8 m at an angle of 26° north of east.
C)7.2 m at an angle of 26° east of north.
D)3.3 m at an angle of 26° north of east.
E)3.3 m at an angle of 64° east of north.

Question 31

The magnitude of
Is 5.5 m,and this vector lies in the second quadrant and makes an angle of 34° with the +y-axis.The components of
Are closest to

A) = -3.1 m,
= 4.6 m.
B) = 3.1 m,
= -4.6 m.
C) = 4.6 m,
= -3.1 m.
D) = -4.6 m,
= 3.1 m.
E) = -4.6 m,
= -3.1 m.

Question 32

A car travels 20 km west and then 20 km south.What is the magnitude of its displacement vector?

A)0 km
B)20 km
C)28 km
D)40 km

Question 33

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)75°
B)57°
C)33°
D)15°

Question 34

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal.What is the horizontal component of the boy's velocity?

A)18.1 m/s
B)15.6 m/s
C)8.45 m/s
D)12.6 m/s
E)9.33 m/s

Question 35

You walk 53 m to the north,then you turn 60° to your right and walk another
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

Question 36

A player throws a football 50.0 m at 61.0° north of west.What is the westward component of the displacement of the football?

A)64.7m
B)55.0 m
C)0.00 m
D)74.0 m
E)24.2 m

Question 37

The components of vectors
And
Are given as follows:
A_x = 7.6 B_x = -5.1
A_y = -9.2 B_y = -6.8
What is the magnitude of the vector difference
-
?

A)13
B)3.5
C)16
D)170
E)3.4

Question 38

A velocity vector has components 36 m/s westward and 22 m/s northward.What are the magnitude and direction of this vector?

Question 39

Vector
= 4.00 m points eastward and vector
= 3.00 m points southward.The resultant vector
+
Is given by

A)5.00 m at an angle of 36.9° south of east.
B)5.00 m at an angle of 53.1° south of east.
C)5.00 m at an angle of 71.6° south of east.
D)5.00 m at an angle of 18.4° south of east.
E)5.00 m at an angle of 26.6° south of east.

Question 40

You walk
To the north,then turn 60° to your right and walk another
How far are you from where you originally started?

A)68 m
B)39 m
C)75 m
D)35 m

Question 41

Three vectors, , ,and ,have the components shown in the table.What angle does the resultant of these three vectors make with the +x-axis?

A)24° above the +x-axis
B)24° below the +x-axis
C)66° above the +x-axis
D)66° below the +x-axis

Question 42

Vector
Has a magnitude of 7.0 m and points 30° east of north.Vector
Has a magnitude of 5.0 m and points 30° west of south.The resultant vector
+
Is given by

A)10.0 m at an angle 60° north of east.
B)10.0 m at an angle 30° east of north.
C)2.0 m at an angle 30° north of east.
D)2.0 m at an angle 60° north of east.
E)1.0 m at an angle 60° east of north.

Question 43

Vector
Has a magnitude of 6.0 m and points 30° north of east.Vector
Has a magnitude of 4.0 m and points 30° west of south.The resultant vector
+
Is given by

A)2.7 m at an angle of 8.3° south of east.
B)2.7 m at an angle of 8.3° east of south.
C)3.2 m at an angle of 8.3° east of south.
D)3.2 m at an angle of 8.3° south of east.
E)2.3 m at an angle of 8.3° south of east.

Question 44

An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h.What is the speed of the plane relative to the ground?

A)90 km/h
B)110 km/h
C)140 km/h
D)150 km/h

Question 45

Vector
Has a magnitude of 8.0 m and points 30° north of east;vector
Has a magnitude of 6.0 m and points 30° west of north;and vector
Has a magnitude of 5.0 m and points 30° west of south.The resultant vector
+
+
Is given by

A)2.7 m at an angle 74° north of east.
B)5.9 m at an angle 74° north of east.
C)4.8 m at an angle 74° east of north.
D)5.1 m at an angle 74° north of east.
E)2.1 m at an angle 66° east of north.

Question 46

Vector
Has a magnitude of 4.0 m and points 30° south of east.Vector
Has a magnitude of 2.0 m and points 30° north of west.The resultant vector
+
Is given by

A)10.0 m at an angle 30° south of east.
B)10.0 m at an angle 60° east of south.
C)2.0 m at an angle 60° south of east.
D)2.0 m at an angle 30° south of east.
E)1.0 m at an angle 30° east of south.

Question 47

A plane has an airspeed of 200 m/s northward,and is in a wind of 50.0 m/s to the west.The plane's speed relative to the ground is

A)150 m/s.
B)200 m/s.
C)206 m/s.
D)250 m/s.

Question 48

Three vectors, , ,and ,have the components shown in the table.What is the magnitude of the resultant of these three vectors?

A)5.50 m
B)13.0 m
C)11.1 m
D)7.00 m
E)2.00 m

Question 49

A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal.At that instant,what is the speed of the projectile with respect to a stationary observer on the ground?

A)245 m/s
B)250 m/s
C)268 m/s
D)293 m/s

Question 50

You are traveling at 55 mi/h along the +x-axis relative to a straight,level road and pass a car that is traveling at 45 mi/h.The relative velocity of your car to the other car is

A)-10 mi/h.
B)10 mi/h.
C)65 mi/h.
D)35 mi/h.

Question 51

Four vectors,
,
,
,and
,are shown in the figure.The sum of these four vectors is a vector having magnitude and direction

A)4.0 cm,along +x-axis.
B)4.0 cm,along -x-axis.
C)4.0 cm,along +y-axis.
D)4.0 cm,along -y-axis.
E)4.0 cm,45° above +x-axis.

Question 52

An airplane undergoes the following displacements,all at the same altitude: First,it flies
In a direction 30.0° east of north.Next,it flies
Due south.Finally,it flies
30.0° north of west.Use components to determine how far the airplane ends up from its starting point.

A)71.5 km
B)73.0 km
C)74.4 km
D)70.1 km
E)68.7 km

Question 53

Vector
Has a magnitude of 6.0 m and points 30° east of south.Vector
Has a magnitude of 4.0 m and points 30° west of north.The resultant vector
+
Is given by

A)2.0 m at an angle of 30° north of west.
B)2.0 m at an angle of 30° east of south.
C)10.0 m at an angle of 60° north of west.
D)10.0 m at an angle of 60° east of south.
E)1.0 m at an angle of 60° north of west.

Question 54

Vector
Has a magnitude of 6.0 m and points 30° south of east.Vector
Has a magnitude of 4.0 m and points 30° west of south.The resultant vector
+
Is given by

A)7.2 m at an angle of 64° south of east.
B)3.3 m at an angle of 64° south of east.
C)9.8 m at an angle of 26° south of east.
D)9.8 m at an angle of 64° south of east.
E)3.3 m at an angle of 26° south of east.

Question 55

The figure shows three vectors and their magnitudes and relative directions.The magnitude of the resultant of the three vectors is closest to

A)19
B)16
C)13
D)10
E)7.0

Question 56

The figure shows four vectors,
,
,
,and
,having magnitudes 12.0 m,10.0 m,8.0 m,and 4.0 m,respectively.The sum of these four vectors is

A)16.4 m at an angle 77.8° with respect to +x-axis.
B)16.4 m at an angle 12.3° with respect to +x-axis.
C)19.5 m at an angle 77.8° with respect to +x-axis.
D)19.5 m at an angle 12.3° with respect to +x-axis.
E)8.20 m at an angle 77.8° with respect to +x-axis.

Question 57

Your motorboat can move at 30 km/h in still water.What is the minimum time it will take you to move 12 km downstream in a river flowing at 6.0 km/h?

A)20 min
B)22 min
C)24 min
D)30 min

Question 58

Three forces,
₁,
₂,and
₃,all act on an object,as shown in the figure.The magnitudes of the forces are: F₁ = 80.0 N,F₂ = 60.0 N,and F₃ = 40.0 N.The resultant force acting on the object is given by

A)180 N at an angle of 60.0° with respect to +x-axis.
B)60.0 N at an angle of 90.0° with respect to +x-axis.
C)20.0 N at an angle of 34.3° with respect to +x-axis.
D)35.5 N at an angle of 34.3° with respect to +x-axis.
E)40.0 N at an angle of 60.0° with respect to +x-axis.

Question 59

Vector
Has a magnitude of 8.0 m and points east,vector
Has a magnitude of 6.0 m and points north,and vector
Has a magnitude of 5.0 m and points west.The resultant vector
+
+
Is given by

A)2.0 m at an angle 63° north of east.
B)2.0 m at an angle 63° east of north.
C)6.7 m at an angle 63° east of north.
D)6.7 m at an angle 63° north of east.
E)3.8 m at an angle 67° north of east.

Question 60

Three forces,
₁,
₂,and
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)35 N.
B)70 N.
C)140 N.
D)210 N.
E)0 N.

Question 61

A boat,whose speed in still water is 8.0 m/s,crosses a river with a current of 6.0 m/s.If the boat heads perpendicular to the current,what is the speed of the boat relative to an observer standing on the shore as it crosses the river?

A)5.3 m/s
B)6.0 m/s
C)8.0 m/s
D)10.0 m/s

Question 62

An airplane flies between two points on the ground that are 500 km apart.The destination is directly north of the point of origin of the flight.The plane flies with an airspeed of 120 m/s.If a constant wind blows at 10 m/s toward the west during the flight,what direction must the plane fly relative to the air to arrive at the destination?

A)4.8° east of north
B)5.9° east of north
C)85° west of north
D)4.8° west of north
E)5.9° west of north

Question 63

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s.During this swim,she is swept downstream 480 m.What is the speed of the current?

A)0.50 m/s
B)0.80 m/s
C)1.2 m/s
D)1.4 m/s
E)1.8 m/s

Question 64

A plane has an eastward heading with an airspeed of 156 m/s.A 20.0 m/s wind is blowing southward at the same time as the plane is flying.The velocity of the plane relative to the ground is

A)157 m/s at an angle 7.31° south of east.
B)157 m/s at an angle 7.31° east of south.
C)155 m/s at an angle 7.36° south of east.
D)155 m/s at an angle 7.36° east of south.
E)157 m/s at an angle 7.36° south of east.

Question 65

On a calm day with no wind,you can run a 1500-m race at a velocity of 4.0 m/s.If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s,how much time would it take you to finish the race?

A)250 s
B)750 s
C)1125 s
D)9000 s

Question 66

A plane has an airspeed of 142 m/s.A 30.0 m/s wind is blowing southward at the same time as the plane is flying.What must be the heading of the plane in order to move directly eastward relative to the ground?

A)78.1° north of east
B)11.9° north of east
C)77.8° north of east
D)12.2° north of east
E)55.3° north of east

Question 67

A plane has an airspeed of 142 m/s.A 16 m/s wind is blowing southward at the same time as the plane is flying.If the velocity of the plane relative to the ground is directly eastward,what is the magnitude of that velocity?

A)130 m/s
B)16 m/s
C)160 m/s
D)141 m/s
E)48 m/s

Question 68

A plane flies directly from city A to city B,which are separated by 2300 mi.From A to B,the plane flies into a 65 mi/h headwind.On the return trip from B to A,the wind velocity is unchanged.The trip from B to A takes
Less than the trip from A to B.What is the airspeed (assumed constant)of the plane relative to the air (that is,the airspeed)?

A)530 mi/h
B)400 mi/h
C)480 mi/h
D)610 mi/h

Question 69

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s.During this swim,she is swept downstream 480 m.How fast can she swim in still water?

A)0.50 m/s
B)0.80 m/s
C)1.2 m/s
D)1.4 m/s
E)1.8 m/s