Deck 1: Introduction and Mathematical Concepts

Question 1

The surface of a lake has an area of 15.5 km².What is the area of the lake in m²?

A)1.55 × 10⁴ m²
B)1.55 × 10⁵ m²
C)1.55 × 10⁶ m²
D)1.55 × 10⁷ m²
E)1.55 × 10⁸ m²

Answer 1

1.55 × 10⁷ m²

Question 2

The Boston Marathon is the oldest annual foot race, in which those that finish complete a distance of 26 miles, 385 yards.Express this distance in kilometers.

A)16.295 km
B)16.398 km
C)42.186 km
D)42.453 km
E)56.496 km

Answer 2

42.186 km

Question 3

The mathematical relationship between three physical quantities is given by .If the dimension of b is; and the dimension of c is [L].Which one of the following choices is the dimension of a?

A)[L]
B)
C)
D)[T]
E)

Answer 3

Question 4

Which one of the following choices is equivalent to 152 m?

A)1.52 × 10¹ m
B)1.52 × 10² m
C)1.52 × 10^-1 m
D)1.52 × 10^-2 m
E)1.52 × 10⁰ m

Question 5

Complete the following statement: The ratio is equal to

A)10².
B)10³.
C)10⁶.
D)10^-3.
E)10^-6.

Question 6

Which one of the following is an SI base unit?

A)gram
B)slug
C)newton
D)centimeter
E)kilogram

Question 7

Which one of the following choices is equivalent to 44.5 mm?

A)4.45 × 10¹ m
B)4.45 × 10^-2 m
C)44.5 × 10^-1 m
D)44.5 × 10^-2 m
E)4.45 × 10⁰ m

Question 8

The mass of a raindrop is 4 milligrams.Which one of the following statements indicates the correct mass of the raindrop in grams?

A)The raindrop has a mass of 4 × 10⁶ grams.
B)The raindrop has a mass of 4 × 10^-3 grams.
C)The raindrop has a mass of 4 × 10^-1 grams.
D)The raindrop has a mass of 4 × 10³ grams.
E)The raindrop has a mass of 4 × 10^-6 grams.

Question 9

Complete the following statement: Today, the standard meter is defined in terms of

A)the distance from the earth's equator to the north pole.
B)the wavelength of light emitted from a krypton atom.
C)the wavelength of light emitted from a sodium atom.
D)a platinum-iridium bar kept in France.
E)the speed of light.

Question 10

Which one of the following pairs of units may not be added together, even after the appropriate unit conversions have been made?

A)grams and milligrams
B)kilometers and kilograms
C)miles and kilometers
D)slugs and kilograms
E)centimeters and yards

Question 11

The distance d that a certain particle moves may be calculated from the expression d = at + bt² where a and b are constants; and t is the elapsed time.What must the dimensions of the quantities a and b be, respectively?

A)
B)[L], [L]²
C)
D)
E)

Question 12

Which one of the following choices is equivalent to 8.0 m²?

A)8.0 × 10^-4 cm²
B)8.0 × 10² cm²
C)8.0 × 10^-2 cm²
D)8.0 × 10⁴ cm²
E)8.0 × 10³ cm²

Question 13

In the sport of horseshoe pitching, two stakes are 40.0 feet apart.What is the distance in meters between the two stakes?

A)24.4 m
B)4.80 m
C)18.3 m
D)12.2 m
E)15.7 m

Question 14

Which one of the following expressions may be used to correctly find the angle $\theta$ in the drawing?

A)
B)
C)
D)
E)

Question 15

Which one of the following is the longest length?

A)10⁰ meters
B)10² centimeters
C)10⁴ millimeters
D)10⁵ micrometers
E)10⁷ nanometers

Question 16

Complete the following statement: Today, the standard unit of time is defined in terms of

A)the electromagnetic waves emitted by cesium atoms.
B)the motion of the moon around the earth.
C)the motion of a precision pendulum.
D)the average solar day.
E)the speed of light.

Question 17

In a diving competition, a woman dives from a platform that is ten meters above the surface of the water.What is the height, expressed in feet, of the platform?

A)13 feet
B)18 feet
C)24 feet
D)33 feet
E)47 feet

Question 18

Complete the following statement: Today, the standard unit of mass is defined in terms of

A)a specified volume of water at 4 °C.
B)a standard platinum-iridium cylinder.
C)a specified number of cesium atoms.
D)a standard platinum bar.
E)the speed of light.

Question 19

A candy shop sells a pound of chocolate for $ 10.85.What is the price of 1.50 kg of chocolate at the shop?

A)$ 8.17
B)$ 13.49
C)$ 17.98
D)$ 29.73
E)$ 35.81

Question 20

A certain physical quantity, R, is calculated using the formula: R = 4a²(b - c) where a, b, and c are distances.What is the SI unit for R?

A)cm
B)cm²
C)m
D)m²
E)m³

Question 21

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

Question 22

A 3.0-m ladder leans against a wall and makes an angle with the wall of 28° as shown in the drawing.What is the height h above the ground where the ladder makes contact with the wall?

A)2.6 m
B)2.3 m
C)2.1 m
D)1.9 m
E)1.6 m

Question 23

A surveyor wants to find the distance across a river.A stake is placed on each bank of the river as shown in the figure.She measures a distance of 30.0 m from one stake to another on the same side of the river, thus finding the third vertex on a right triangle.She then measures the angle $\theta$ and finds it equal to 75.9°.What is the distance across the river?

A)89.2 m
B)15.3 m
C)119 m
D)268 m
E)29.0 m

Question 24

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

A)two
B)three
C)four
D)five
E)six

Question 25

A certain mountain road is inclined 3.1° with respect to the horizon.What is the change in altitude of the car as a result of its traveling 2.90 km along the road?

A)157 m
B)181 m
C)116 m
D)203 m
E)289 m

Question 26

A student adds two displacement vectors with magnitudes of 6.0 m and 8.0 m, respectively. Which one of the following could not be a possible choice for the resultant?

A)2.3 m
B)6.6 m
C)10.0 m
D)12.8 m
E)14.8 m

Question 27

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 be displacements.
B) and must have equal lengths.
C) and must point in opposite directions.
D) and must point in the same direction.
E) and must be at right angles to each other.

Question 28

Three sticks are arranged to form a right triangle.If the lengths of the three sticks are 0.47 m, 0.62 m and 0.78 m, what are the three angles of the triangle?

A)90°, 45°, and 45°
B)90°, 62°, and 28°
C)90°, 59°, and 31°
D)90°, 48°, and 42°
E)90°, 53°, and 37°

Question 29

City A lies 30 km directly south of city B.A bus, beginning at city A travels 50 km at 37° north of east to reach city C.How far and in what direction must the bus go from city C to reach city B?

A)20 km, west
B)40 km, west
C)80 km, west
D)40 km, east
E)80 km, east

Question 30

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 have equal magnitudes and point in opposite directions.
B) and have equal magnitudes and point in the same direction.
C) and have equal magnitudes and point in opposite directions.
D) and point in the same direction, but
has twice the magnitude of
.
E) and point in the same direction, but
has twice the magnitude of
.

Question 31

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.

Question 32

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)It must be 10.0 km.
B)It must be 14.0 km.
C)It could be equal to zero kilometers, depending on how the vectors are oriented.
D)No conclusion can be reached without knowing the directions of the vectors.
E)It could have any value between 2.0 km and 14.0 km depending on how the vectors are oriented.

Question 33

A pole is held vertically by attaching wires at a height of 13.4 m above the ground.The other end of each wire is anchored in the ground at a distance of 9.54 m from the base of the pole.The pole makes a right angle with the ground.What is the length of each wire?

A)14.1 m
B)19.7 m
C)11.5 m
D)16.4 m
E)22.8 m

Question 34

The length of each side of a square is 4.0 m.What is the length of the diagonal of the square (shown as a dashed line in the figure)?

A)2.8 m
B)8.0 m
C)5.7 m
D)6.8 m
E)16 m

Question 35

Which one of the following choices is a vector quantity?

A)mass
B)temperature
C)time
D)displacement
E)volume

Question 36

Which one of the following quantities is a vector quantity?

A)the age of the earth
B)the mass of a freight train
C)the earth's pull on your body
D)the temperature of an iced coffee
E)the number of people attending a soccer game

Question 37

Which expression is false concerning the vectors shown in the sketch?

A) = +

B) + = -

C) + +
= 0
D)C < A + B
E)A ² + B ² = C ²

Question 38

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 statement concerning these vectors is true?

A) and must be at right angles to each other.
B) and could have any orientation relative to each other.
C) and must have equal lengths.
D) and must be parallel.
E) and could be antiparallel.

Question 39

What is the angle between the vectors and - when they are drawn from a common origin?

A)0°
B)90°
C)180°
D)270°
E)360°

Question 40

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

A)two
B)three
C)four
D)five
E)six

Question 41

A vector has a magnitude of 40.0 units and points 35.0° above the positive x axis.A second vector 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 = + .

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

Question 42

Which one of the following answers would give the correct number of significant figures when the following masses are added together: 3.6 kg, 113 kg, and 4.19 kg?

A)121 kg
B)120.8 kg
C)120.79 kg
D)1.20 × 10² kg
E)120.8 × 10³ kg

Question 43

Town A lies 20 km north of town B.Town C lies 13 km west of town A.A small plane flies directly from town B to town C.What is the displacement of the plane?

A)33 km, 33° north of west
B)19 km, 33° north of west
C)24 km, 57° north of west
D)31 km, 57° north of west
E)6.6 km, 40° north of west

Question 44

A displacement vector has a magnitude of 810 m and points at an angle of 18° above the positive x axis.What are the x and y scalar components of this vector? x scalar component y scalar component

A)770 m 250 m
B)560 m 585 m
C)585 m 560 m
D)250 m 750 m
E)713 m 385 m

Question 45

A physics text has 544 sheets (1088 pages) and is 34.3 millimeters thick between the inside front cover and the inside back cover.What is the thickness of a single sheet?

A)6.36 × 10^-4 m
B)3.16 × 10^-2 m
C)6.28 × 10^-3 m
D)7.24 × 10^-6 m
E)6.30 × 10^-5 m

Question 46

During the execution of a play, a football player carries the ball for a distance of 33 m in the direction 58° 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

Question 47

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

Question 48

Use the component method of vector addition to find the components of the resultant of the four displacements shown in the figure.The magnitudes of the displacements are: A = 2.25 cm, B = 6.35 cm, C = 5.47 cm, and D = 4.19 cm. x component y component

A)2.19 cm -6.92 cm
B)3.71 cm -1.09 cm
C)5.45 cm -2.82 cm
D)1.09 cm -3.71 cm
E)6.93 cm -2.19 cm

Question 49

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: = 2.0 km, east; = 5.2 km, north; = 4.9 km, west; = 3.0 km, south What is the resultant displacement of the members of the bicycle club: = + + + ?

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

Question 50

A bird flies 25.0 m in the direction 55° east of south to its nest on a cliff.The bird then flies 75.0 m in the direction 55° west of north to the top of a tree.What are the northward and westward components of the resultant displacement of the bird from its nest? northward westward

A)29 m 41 m
B)41 m 29 m
C)35 m 35 m
D)81 m 57 m
E)57 m 81 m

Question 51

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

Question 52

Use the component method of vector addition to find the resultant of the following three vectors: = 56 km, east = 11 km, 22° south of east = 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

Question 53

A runaway dog walks 0.64 km due north.He then runs due west to a hot dog stand.If the magnitude of the dog's total displacement vector is 0.91 km, what is the magnitude of the dog's displacement vector in the due west direction?

A)0.27 km
B)0.33 km
C)0.41 km
D)0.52 km
E)0.65 km

Question 54

A bug crawls 2.25 m along the base of a wall.Upon reaching a corner, the bug's direction of travel changes from south to west.The bug then crawls 3.15 m before stopping.What is the magnitude of the bug's displacement?

A)5.40 m
B)2.72 m
C)3.87 m
D)4.11 m
E)3.29 m

Question 55

A race car will make one lap around a circular track of radius R.When the car has traveled halfway around the track, what is the magnitude of the car's displacement from the starting point?

A)2R
B)R
C)( $\pi$ R)
D)(2 $\pi$ R)
E)zero meters

Question 56

The x and y components of a displacement vector are -3.00 m and +4.00 m, respectively.What angle does this vector make with the positive x axis?

A)233°
B)127°
C)-53.0°
D)53.0°
E)37.0°

Question 57

A sailboat leaves a harbor and sails 1.8 km in the direction 65° south of east, where the captain stops for lunch.A short time later, the boat sails 1.1 km in the direction 15° north of east.What is the magnitude of the resultant displacement from the harbor?

A)2.3 km
B)1.5 km
C)2.9 km
D)1.2 km
E)0.59 km

Question 58

Two vectors and , are added together to form the vector = + .The relationship between the magnitudes of these vectors is given by: C_x = A cos 30° + B and C_y = -A sin 30°.Which statement best describes the orientation of these vectors?

A) points in the negative x direction while points in the positive y direction.
B) points in the negative y direction while points in the positive x direction.
C) points 30° below the positive x axis while points in the positive x direction.
D) points 30° above the positive x axis while points in the positive x direction.
E) points 30° above the negative x axis while points in the positive x direction.

Question 59

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.

Question 60

A force, , of magnitude 2.0 N and directed due east is exerted on an object.A second force exerted on the object is = 2.0 N, due north.What is the magnitude and direction of a third force, , 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

Question 61

1-1
Two vectors, and , are added together to form the vector = + .
The relationship between the magnitudes of these vectors is given by:
C_x = 0
C_y = A sin 60° + B sin 30°
A_x and A_y point in the positive x and y directions, respectively.
Which one of the following statements best describes the orientation of vectors and ?

A) and point in opposite directions.
B) points 60° above the positive x axis while points 30° above the negative x axis.
C) points 60° above the negative x axis while points 30° above the positive x axis.
D) points 60° below the positive x axis while points 30° above the positive y axis.
E) points 60° below the positive x axis while points 30° below the positive y axis.

Question 62

1-3
A boat radioed a distress call to a Coast Guard station.At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north.A vector from the station to the point where the boat was later found is = 30.0 km, 15.0° north of east.
What are the components of the vector from the point where the distress call was made to the point where the boat was found? In other words, what are the components of vector = - ? x component y component

A)35.7 km, west 17.4 km, north
B)40.6 km, east 51.2 km, south
C)17.3 km, west 51.2 km, south
D)40.6 km, east 35.7 km, north
E)17.3 km, east 35.7 km, south

Question 63

How does the magnitude of compare with that of ?

A)A = B
B)A = 1.7B
C)A = 0.4B
D)A = 0.5B
E)A = 0.7B

Question 64

Determine the magnitude of the vector sum, + .

A)5 units
B)15 units
C)20 units
D)30 units
E)50 units

Question 65

How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector ?

A)65.3 km
B)39.7 km
C)26.5 km
D)54.0 km
E)42.5 km

Question 66

Justine and her friends exit the physics classroom and walk 0.70 km to their math class.While walking, Justine's average step length is 58 cm.Approximately, how many steps does she take in walking between these two classes?

A)310
B)720
C)1200
D)3100
E)7200

Question 67

Determine the magnitude of the vector difference, - .

A)5 units
B)15 units
C)20 units
D)30 units
E)50 units