Deck 1: Units, Trigonometry, and Vectors

Question 1

A city uses 6.8 × 10⁹ gallons​ of water every day.How many gallons per minute must be pumped from the reservoir to meet the city's water needs?

A)​4.7E+6
B)​7.9E+4
C)​2.8E+8
D)​6.8E+9

Answer 1

​4.7E+6

Question 2

The prefixes which are abbreviated f,d,and T represent which of the following?

A)10^-30,10^-2,and 10²⁴
B)10^-15,10²,and 10²⁴
C)10^-15,10^-1,and 10¹²
D)10^-13,10²,and 10²⁴
E)1​0^-30,10^-1,and 10^-2

Answer 2

10^-15,10^-1,and 10¹²

Question 3

Areas always have dimensions ____ while volumes always have dimensions ____.

A)m²,m³
B)L²,L³
C)Both a and b are correct.
D)No answer is correct because of the "always."

Answer 3

L²,L³

Question 4

The proton contains which of the following combination of quarks?

A)two up quarks and one down quark
B)one up quark and two down quarks
C)one top quark and two bottom quarks
D)two top quarks and one bottom quark

Question 5

The nuclei of atoms contain

A)electrons only.
B)neutrons only.
C)protons and electrons.
D)protons and neutrons.

Question 6

Since 1967 the standard definition for the second has been based on which of the following?

A)characteristic frequency of the cesium-133 atom
B)average solar day
C)sidereal day
D)Greenwich Civil Time
E)None of the above

Question 7

​A herd of sheep eats 10 bales of hay every 4 days.If a bale of hay costs $2.85,how much will it cost to feed the sheep hay for one year?

A)​$912.50
B)​$2,600.63
C)​$28.50
D)​$3,650.00

Question 8

Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration,x is distance,and t is time)

A)v/t²
B)vx²
C)v²/t
D)at

Question 9

In 1983 the standard meter was redefined to what it is currently.What was the previous definition from 1960 based on?

A)specific alloy bar housed at Sevres,France
B)wavelength of light emitted by certain krypton atoms
C)distance from the Earth's equator to the North Pole
D)the distance light travels in a certain fraction of a second

Question 10

Since 1983 the standard meter has been defined in terms of which of the following?​

A)specific alloy bar housed at Sevres,France
B)wavelength of light emitted by krypton-86
C)distance from the Earth's equator to the North Pole
D)the distance light travels in a certain fraction of a second
E)None of the above

Question 11

The speed of a boat is often given in knots.If a speed of 5 knots were expressed in the SI system of units,the units would be:

A)m.
B)s.
C)m/s.
D)kg/s.

Question 12

​Which is smallest,an atom,a nucleus,a proton,or an electron?

A)​atom
B)​electron
C)​nucleus
D)​proton

Question 13

If the displacement of an object,x,is related to velocity,v,according to the relation x = Av,the constant,A,has the dimension of which of the following?

A)acceleration
B)length
C)time
D)area

Question 14

In mechanics,physicists use three basic quantities to derive additional quantities.Mass is one of the three quantities.What are the other two?

A)length and force
B)power and force
C)length and time
D)force and time

Question 15

When was the existence of the neutron confirmed?

A)in ancient times
B)in 1895
C)in 1932
D)in 1969

Question 16

The ratio T/m of the prefixes M and m has what value?

A)10¹⁶
B)10¹⁴
C)10¹⁵
D)10¹³
E)​10¹⁷

Question 17

One mole of ammonia (NH₃)has a mass of 17.0 g,and one mole is equal to 6.02 × 10²³ molecules.How many hydrogen (H)atoms are in 55.0 g of ammonia? Note that each molecule of ammonia has 3 hydrogen atoms.

A)​5.84E+24
B)​1.95E+24
C)​3.07E+25
D)​6.49E+23

Question 18

If a is acceleration,v is velocity,x is position,and t is time,then which equation is not dimensionally correct?

A)t = x/v
B)a = v²/x
C)v = a/t
D)t² = 2x/a

Question 19

Sphere A has a radius of 5.00 cm,and sphere B has a radius of 8.80 cm.What is the difference in volume between the two spheres? ​

A)​2 330 cm³
B)​556 cm³
C)​6 990 cm³
D)​165 cm³

Question 20

Which expression is dimensionally consistent with an expression that would yield a value for time−¹? (v is velocity,x is distance,and t is time)

A)v/x
B)v²/x
C)x/t
D)v²t

Question 21

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 8 and 9 cm,how many significant figures will result if you only use the part of the meter stick between the 82-cm and 93-cm positions?

A)0
B)2
C)3
D)4
E)​more than 4

Question 22

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 25 and 53 cm,how many significant figures will result if you only use the part of the meter stick between the 3-cm and 85-cm positions?

A)1
B)2
C)3
D)4
E)​more than 4

Question 23

There are other ways of expressing uncertainty besides significant figures.For example,suppose a quantity is known to have a value between 20.4 and 20.0,and our best estimate of the value is midrange at 20.2.We could write the number as 20.2 +/− 0.2 and say that the number has a 1% uncertainty.We would also say it has 3 significant figures.If we square a number with 1% uncertainty and 3 significant figures,what results?

A)A number with 1% uncertainty and 3 significant figures.
B)A number with 2% uncertainty and 3 significant figures.
C)A number with 2% uncertainty and 2 significant figures.
D)A number with 1% uncertainty and 2 significant figures.

Question 24

Suppose an equation relating position,x,to time,t,is given by x = bt³ + ct⁴,where b and c are constants.The dimensions of b and c are respectively:

A)T³,T⁴.
B)1/T³,1/T⁴.
C)L/T³,L/T⁴.
D)L²⋅T³,L²⋅T⁴.

Question 25

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 15.0 × 5.6 × 2.33?

A)200
B)195.720
C)195.72
D)​195.7
E)​196

Question 26

When SI units are plugged into an equation,it is found that the units balance.Which of the following can we expect to be true for this equation?

A)The equation will be dimensionally correct.
B)The equation will be dimensionally correct except sometimes in cases when the right-hand side of the equation has more than one term.
C)The equation will not be dimensionally correct.
D)All constants of proportionality will be correct.

Question 27

​A rectangular-shaped patio has a base length equal to (24.5 ± 0.2)m and a height equal to (9.3 ± 0.1)m.What is the area of the patio,including its uncertainty?

A)​228 ± 4
B)​228 ± 2
C)​228 ± 23
D)​228 ± 6

Question 28

Calculate (0.83 + 0.049)(4.4 × 10³),keeping only significant figures.

A)3 900
B)3 868
C)3 886
D)​3 644
E)​4 000

Question 29

A cement truck can pour 160 cubic yards of cement per hour.Express this in ft³/min.

A)480 ft³/min
B)2.67 ft³/min
C)24.0 ft³/min
D)8.00 ft³/min
E)​72.0 ft³/min

Question 30

The length and width of a standard sheet of paper is measured,and then the area is found by calculation to be 91.50 in.².The number of significant figures in the width measurement must be at least

A)1.
B)2.
C)3.
D)4.
E)​5.

Question 31

How many significant figures does the number 3 600 have?​

A)1
B)2
C)3
D)4
E)​One cannot tell with certainty when the number is written in the given form,but it will be one of the other given answers.

Question 32

A cereal box has the dimensions of 0.14 m × 0.22 m × 0.070 m.If there are 3.28 feet per meter,then what is the volume of the box in cubic feet?

A)7.6E-2 cubic feet
B)2.3E-2 cubic feet
C)2.7E-1 cubic feet
D)3.9E-3 cubic feet
E)​1.3E-2 cubic feet

Question 33

Multiplying a 2-significant-figure number by a 4-significant-figure number and then dividing the product by a seven-significant-figure number yields a number with how many significant figures?

A)6/7
B)1
C)2
D)13
E)​8/7

Question 34

Volume can be measured in units of m³.Which of the following unit combinations also result in volume?

A)ft²/m
B)cm·ft
C)cm²in.
D)m²·cm·ft

Question 35

The number 0.03 has how many significant figures?

A)2
B)3
C)5
D)6
E)​7

Question 36

The basic function of an automobile's carburetor is to atomize the gasoline and mix it with air to promote rapid combustion.Assume that 30.0 cm³ of gasoline is atomized into N spherical droplets.Each droplet has a radius of 1.0 × 10−⁵ m.Find the total surface area of these N spherical droplets.​

A)3.0E+4 cm²
B)1.2E+5 cm²
C)1.8E+5 cm²
D)9.0E+4 cm²
E)​1.1E+5 cm²

Question 37

Modern electroplaters can cover a surface area of 75.0 m² with one troy ounce of gold (volume = 1.611 cm³).What is the thickness of the electroplated gold?

A)2.15E-8 m
B)1.07E-8 m
C)1.43E-8 m
D)4.30E-8 m
E)​None of the above

Question 38

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 6 and 7 cm,how many significant figures will result if you only use the part of the meter stick between the 1-cm and 9-cm positions?

A)2
B)3
C)4
D)5
E)​more than 5

Question 39

On planet Z,the standard unit of length is the foose.Ann the Astronaut is 5.2 feet tall on Earth.She lands on planet Z and is measured to be 88 foosi tall.Her partner Rachael is 92 foosi tall.How tall is Rachael on Earth?​

A)5.9 feet
B)5.4 feet
C)5.2 feet
D)5.1 feet
E)5.6​ feet

Question 40

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 15.9 + 14 + 77.68 + 6.898?

A)​114.4780
B)​114.478
C)​114.48
D)​114.5
E)​114

Question 41

A room in a house has a floor area of 110 ft².Which of the following is most likely the approximate volume of the room?

A)3 m³
B)30 m³
C)300 m³
D)3 000 m³
E)​10 m³

Question 42

A physics class in a large lecture hall has 150 students.The total mass of the students is about ____ kg.

A)10⁴
B)10⁵
C)10⁶
D)10⁷
E)​10⁸

Question 43

​The distance from New York to London is 3 470 miles.If a plane takes 6.0 hours to fly this distance,what is the plane's average speed in kilometers per hour? 1 mile = 1.609 km.

A)​2 200
B)​620
C)​390
D)​930

Question 44

When NASA was communicating with astronauts on the Moon,the time from sending on the Earth to receiving on the Moon was 1.28 s.Find the distance from Earth to the Moon.(The speed of radio waves is 3.00 × 10⁸ m/s. )

A)240 000 km
B)384 000 km
C)480 000 km
D)768 000 km

Question 45

The information on a one-gallon paint can is that the coverage,when properly applied,is 440 ft².One gallon is 231 in³.What is the average thickness of the paint in such an application?

A)3.6E-3 in
B)5.3E-1 in
C)4.4E-2 in
D)1.3E-2 in
E)​1.6E-1 in

Question 46

​A marble has a radius of 16 mm.Approximately how many marbles will fit in a cube-shaped container with each side equal to 36 cm?

A)​20
B)​510
C)​1 420
D)​80

Question 47

​Amir drives his ATV from coordinates (5.0 km,25°)directly to (25.0 km,45°)in 45 minutes.What is the ATV's speed?

A)​0.5 km/h
B)​20.4 km/h
C)​27.2 km/h
D)​34.0 km/h

Question 48

An apartment has 1 100 ft² of floor space.What is the approximate volume of the apartment?

A)10² ft³
B)10³ ft³
C)10⁴ ft³
D)10⁵ ft³
E)10⁶ ft³

Question 49

A mosquito flies diagonally from a corner at the floor of a rectangular room,with coordinates (0,0,0)to the opposite corner at the ceiling,with coordinates (5.5,3.75,h)m at a rate of 0.8 m/s.If it takes the mosquito 11 seconds to make the direct flight,what is h? ​

A)​5.8 m
B)​6.7 m
C)​8.5 m
D)​8.3 m

Question 50

​Approximately how many water molecules are in a lake with a volume of 12 100 km³? A water molecule measures approximately 2.75 × 10¯¹⁰ m in length.

A)​2E+15
B)​5E+22
C)​4E+14
D)​6E+41

Question 51

A furlong is a distance of 220 yards.A fortnight is a time period of two weeks.A race horse is running at a speed of 6.00 yards per second.What is his speed in furlongs per fortnight?​

A)3.30E+4 furlongs/fortnight
B)4.71E+3 furlongs/fortnight
C)3.31E+4 furlongs/fortnight
D)3.33E+4 furlongs/fortnight
E)3.28E+4 furlongs/fortnight

Question 52

For which of the values below is x > x⁷?

A)x = -2.0
B)x = 0
C)x = 1.0
D)x = 2.0
E)​x = 4.0

Question 53

Which point is nearest the x-axis?

A)​(1,7)
B)(-3,-6)
C)​(-7,5)
D)​(-6,-4)
E)​(2,3)

Question 54

The mass of a star is 8.0 × 10³⁰ kg,and the mass of a hydrogen atom is 1.67 × 10−²⁷ kg.If we assume that the star is mostly composed of hydrogen,approximately how many atoms are there in the star?

A)1.3E+4 atoms
B)2.1E-58 atoms
C)4.8E+57 atoms
D)8.0E+30 atoms

Question 55

On planet Q the standard unit of volume is called the guppy.Space travelers from Earth have determined that one liter = 39.0 guppies.How many guppies are in 230 liters?​

A)8 970 guppies
B)9 010 guppies
C)8 740 guppies
D)9 200 guppies
E)​8 930 guppies

Question 56

The distance to a hypothetical galaxy is estimated at about 7 × 10⁶ light years.A light year is the distance traveled by light in one year;if the speed of light is 3 × 10⁸ m/s,about how far is it from our galaxy to this hypothetical galaxy? (1 year = 3.15 × 10⁷ s)

A)7E+21 m
B)1E+9 m
C)7E+22 m
D)7E+5 m

Question 57

How long has it been that scientists have accepted that the nucleus of the atom consists of neutrons and protons? Think of your answers in terms of order of magnitude.

A)about a decade
B)about a century
C)about a thousand years
D)since Aristotle

Question 58

​What is the distance between the two polar coordinates (2.0,30°)and (9.0,145°)?

A)​6.0
B)​10.0
C)​9.8
D)​9.2

Question 59

Assume everyone in the United States consumes one soft drink in an aluminum can every two days.If there are 270 million Americans,about how many tons of aluminum need to be recycled each year if each can weighs 1/15 pound and one ton = 2 000 pounds?

A)450 000 tons
B)1.6 million tons
C)3.3 million tons
D)0.82 million tons
E)​410 000 tons

Question 60

Water flows into a swimming pool at the rate of 7.0 gal/min.The pool is 17 ft wide,32 ft long and 7.0 ft deep.How long does it take to fill? (1 U.S.gallon = 231 cubic inches)

A)34 hours
B)68 hours
C)67 hours
D)136 hours
E)​680 hours

Question 61

If point A is located at coordinates (-10,7)and point B is located at coordinates (8,-8),what is the distance from A to B if the units of the coordinated system are meters?

A)549 m
B)23 m
C)28 m
D)33 m
E)​26 m

Question 62

Two wires support a post,with dimensions as shown in the figure.If d = 14 m,what is the value of x?

A)7.5 m
B)6.5 m
C)18.3 m
D)5.2 m

Question 63

A triangle has sides of length 7 cm and 11 cm.If the triangle is a right triangle,which of the following could be the length of the third side,to the nearest centimeter?

A)11 cm
B)8 cm
C)16 cm
D)17 cm
E)​7 cm

Question 64

A high fountain of water is in the center of a circular pool of water.You walk the circumference of the pool and measure it to be 190 meters.You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain.It is 55°.How high is the fountain?

A)25 m
B)53 m
C)86 m
D)43 m
E)48 m

Question 65

​Which of the following is not a vector quantity?

A)​mass
B)​acceleration
C)​displacement
D)​velocity

Question 66

Which of the following is an example of a vector quantity?

A)velocity
B)temperature
C)volume
D)mass

Question 67

When three vectors are added graphically and form a closed triangle,the largest enclosed angle between any two of the vectors cannot be greater than

A)60°.
B)90°.
C)180°.
D)No maximum exists.

Question 68

​A surveyor stands 100 m from the base of a building,and uses a transit to determine that the angle of elevation to the building's roof is 19.0°.If the transit height is 0.80 m,what is the height of the building?

A)​94.6 m
B)​95.4 m
C)​35.2 m
D)​34.4 m

Question 69

If ϕ = 90° − θ,what is the value of sin² ϕ + sin² θ?

A)0
B)1
C)−1
D)​The answer depends on θ.

Question 70

If θ and φ are each first quadrant angles,which of the following must be true if sin θ = cos φ?

A)θ + φ = π rad
B)θ + φ = 90°
C)θ - φ = π/2 rad
D)θ = φ

Question 71

A right triangle has sides 10 m,5 m,and 11 m.The smallest angle of this triangle is nearest

A)32°.
B)27°.
C)22°.
D)63°.
E)​Not attainable since this is not a right triangle.

Question 72

Each edge of a cube has a length of 12.7 cm.What is the length of a diagonal of the cube going through the center of the cube?

A)24.0 in.
B)22.0 in.
C)25.5 in.
D)20.5 in.
E)​8.7 in.

Question 73

A train slowly climbs a 400-m mountain track which is at an angle of 8.0° with respect to the horizontal.How much altitude does it gain?

A)55.7 m
B)200 m
C)60.7 m
D)396 m
E)​400 m

Question 74

When we subtract a velocity vector from another velocity vector,the result is

A)another velocity.
B)an acceleration.
C)a displacement.
D)a scalar.

Question 75

Consider the cosine of any angle between 35° and 40°.If the angle were doubled,what would happen to the cosine of the angle.

A)It would halve.
B)It would decrease to less than half its original value.
C)It would decrease but be more than half its original value.
D)In different cases,it could do any of the above.

Question 76

Consider the sine of any angle between 30° and 40°.If the angle were doubled,what would happen to the sine of the angle?

A)It would double.
B)It would more than double.
C)It would increase but be less than double.
D)In different cases,it could do any of the above.

Question 77

When we add a displacement vector to another displacement vector,the result is

A)a velocity.
B)an acceleration.
C)another displacement.
D)a scalar.

Question 78

Suppose the interior angles of a triangle are φ1,φ₂,and φ₃,with φ1 > φ_{2 >} φ₃.Which side of the triangle is the shortest?

A)The side opposite φ1.
B)The side opposite φ₂.
C)The side opposite φ₃.
D)More information is needed unless the triangle is a right triangle.

Question 79

Vector
Points north,and vector
Points east.If
=
−
,then vector
Points

A)north of east.
B)south of east.
C)north of west.
D)south of west.

Question 80

Which type of quantity is characterized by both magnitude and direction?

A)scalar
B)vector
C)trigonometric
D)algebraic variable