University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

Chapter 1

Overview - all with Video Answers

Educators

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Chapter Questions

Problem 1

Which of the following is the frequency of high C?
a) $376 \mathrm{~g}$
b) $483 \mathrm{~m} / \mathrm{s}$
c) $523 \mathrm{~Hz}$
d) 26.5 J

Krystal K

Krystal K

Numerade Educator

Problem 2

If $\vec{A}$ and $\vec{B}$ are vectors and $\vec{B}=-\vec{A},$ which of the following is true?
a) The magnitude of $\vec{B}$ is equal to the negative of the magnitude of $\vec{A}$.
b) $\vec{A}$ and $\vec{B}$ are perpendicular.
c) The direction angle of $\vec{B}$ is equal to the direction angle of $\vec{A}$ plus $180^{\circ}$
d) $\vec{A}+\vec{B}=2 \vec{A}$.

Tyler Moulton

Numerade Educator

Problem 3

Compare three SI units: millimeter, kilogram, and microsecond. Which is the largest?
a) millimeter
c) microsecond
b) kilogram
d) The units are not comparable.

Averell Hause

Carnegie Mellon University

Problem 4

What is(are) the difference(s) between 3.0 and $3.0000 ?$
a) 3.0000 could be the result from an intermediate step in a calculation; 3.0 has to result from a final step.
b) 3.0000 represents a quantity that is known more precisely than 3.0
c) There is no difference.
d) They convey the same information, but 3.0 is preferred for ease of writing

Tyler Moulton

Numerade Educator

Problem 5

A speed of $7 \mathrm{~mm} / \mu \mathrm{s}$ is equal to:
a) $7000 \mathrm{~m} / \mathrm{s}$
b) $70 \mathrm{~m} / \mathrm{s}$
c) $7 \mathrm{~m} / \mathrm{s}$
d) $0.07 \mathrm{~m} / \mathrm{s}$

Tyler Moulton

Numerade Educator

Problem 6

1.6 A hockey puck, whose diameter is approximately 3 inches, is to be used to determine the value of $\pi$ to three significant figures by carefully measuring its diameter and its circumference. For this calculation to be done properly, the measurements must be made to the nearest _____________.
a) hundredth of a $\mathrm{mm}$
c) $\mathrm{mm}$
e) in
b) tenth of a $\mathrm{mm}$
d) $\mathrm{cm}$

Averell Hause

Carnegie Mellon University

Problem 7

What is the sum of $5.786 \cdot 10^{3} \mathrm{~m}$ and $3.19 \cdot 10^{4} \mathrm{~m} ?$
a) $6.02 \cdot 10^{23} \mathrm{~m}$
c) $8.976 \cdot 10^{3} \mathrm{~m}$
b) $3.77 \cdot 10^{4} \mathrm{~m}$
d) $8.98 \cdot 10^{3} \mathrm{~m}$

Tyler Moulton

Numerade Educator

Problem 8

What is the number of carbon atoms in 0.5 nanomoles of carbon? One mole contains $6.02 \cdot 10^{23}$ atoms.
a) $3.2 \cdot 10^{14}$ atoms
d) $3.2 \cdot 10^{17}$ atoms
b) $3.19 \cdot 10^{14}$ atoms
e) $3.19 \cdot 10^{17}$ atoms
c) $3 . \cdot 10^{14}$ atoms
f) $3 . \cdot 10^{17}$ atoms

Surendra Kumar

Numerade Educator

Problem 9

The resultant of the two-dimensional vectors $(1.5 \mathrm{~m}, 0.7 \mathrm{~m})$, $(-3.2 \mathrm{~m}, 1.7 \mathrm{~m}),$ and $(1.2 \mathrm{~m},-3.3 \mathrm{~m})$ lies in quadrant _________.
a) I
b) II
c) III
d) IV

Tyler Moulton

Numerade Educator

Problem 10

By how much does the volume of a cylinder change if the radius is halved and the height is doubled?
a) The volume is quartered.
d) The volume doubles.
b) The volume is cut in half.
e) The volume
c) There is no change in the volume. quadruples.

Tyler Moulton

Numerade Educator

Problem 11

In Europe, cars' gas consumption is measured in liters per 100 kilometers. In the United States, the unit used is miles per gallon.
a) How are these units related?
b) How many miles per gallon does your car get if it consumes 12.2 liters per 100 kilometers?
c) What is your car's gas consumption in liters per 100 kilometers if it gets 27.4 miles per gallon?
d) Can you draw a curve plotting miles per gallon versus liters per 100 kilometers? If yes, draw the curve.

Averell Hause

Carnegie Mellon University

Problem 12

If you draw a vector on a sheet of paper, how many components are required to describe it? How many components does a vector in real space have? How many components would a vector have in a four-dimensional world?

Tyler Moulton

Numerade Educator

Problem 13

Since vectors in general have more than one component and thus more than one number is used to describe them, they are obviously more difficult to add and subtract than single numbers. Why then work with vectors at all?

Tyler Moulton

Numerade Educator

Problem 14

If $\vec{A}$ and $\vec{B}$ are vectors specified in magnitude-direction form, and $\vec{C}=\vec{A}+\vec{B}$ is to be found and to be expressed in magnitude-direction form, how is this done? That is, what is the procedure for adding vectors that are given in magnitudedirection form?

Averell Hause

Carnegie Mellon University

Problem 15

Suppose you solve a problem and your calculator's display reads $0.0000000036 .$ Why not just write this down? Is there any advantage to using the scientific notation?

Tyler Moulton

Numerade Educator

Problem 16

Since the British system of units is more familiar to most people in the United States, why is the international (SI) system of units used for scientific work in the United States?

Tyler Moulton

Numerade Educator

Problem 17

Is it possible to add three equal-length vectors and obtain a vector sum of zero? If so, sketch the arrangement of the three vectors. If not, explain why not.

Tyler Moulton

Numerade Educator

Problem 18

Is mass a vector quantity? Why or why not?

Tyler Moulton

Numerade Educator

Problem 19

Two flies sit exactly opposite each other on the surface of a spherical balloon. If the balloon's volume doubles, by what factor does the distance between the flies change?

Tyler Moulton

Numerade Educator

Problem 20

What is the ratio of the volume of a cube of side $r$ to that of a sphere of radius $r$ ? Does your answer depend on the particular value of $r ?$

Tyler Moulton

Numerade Educator

Problem 21

Consider a sphere of radius $r$. What is the length of a side of a cube that has the same surface area as the sphere?

Tyler Moulton

Numerade Educator

Problem 22

The mass of the Sun is $2 \cdot 10^{30} \mathrm{~kg}$, and the Sun contains more than $99 \%$ of all the mass in the solar system. Astronomers estimate there are approximately 100 billion stars in the Milky Way and approximately 100 billion galaxies in the universe. The Sun and other stars are predominantly composed of hydrogen; a hydrogen atom has a mass of approximately $2 \cdot 10^{-27} \mathrm{~kg}$.
a) Assuming that the Sun is an average star and the Milky Way is an average galaxy, what is the total mass of the universe?
b) Since the universe consists mainly of hydrogen, can you estimate the total number of atoms in the universe?

Tyler Moulton

Numerade Educator

Problem 23

A futile task is proverbially said to be "like trying to empty the ocean with a teaspoon." Just how futile is such a task? Estimate the number of teaspoonfuls of water in the Earth's oceans.

Averell Hause

Carnegie Mellon University

Problem 24

The world's population passed 6.5 billion in $2006 .$ Estimate the amount of land area required if each person were to stand in such a way as to be unable to touch another person. Compare this area to the land area of the United States, 3.5 million square miles, and to the land area of your home state (or country).

Averell Hause

Carnegie Mellon University

Problem 25

Advances in the field of nanotechnology have made it possible to construct chains of single metal atoms linked one to the next. Physicists are particularly interested in the ability of such chains to conduct electricity with little resistance. Estimate how many gold atoms would be required to make such a chain long enough to wear as a necklace. How many would be required to make a chain that encircled the Earth? If 1 mole of a substance is equivalent to roughly $6.022 \cdot 10^{23}$ atoms, how many moles of gold are required for each necklace?

Tyler Moulton

Numerade Educator

Problem 26

One of the standard clichés in physics courses is to talk about approximating a cow as a sphere. How large a sphere makes the best approximation to an average dairy cow? That is, estimate the radius of a sphere that has the same mass and density as a dairy cow.

Tyler Moulton

Numerade Educator

Problem 27

Estimate the mass of your head. Assume that its density is that of water, $1000 \mathrm{~kg} / \mathrm{m}^{3}$

Tyler Moulton

Numerade Educator

Problem 28

Estimate the number of hairs on your head.

Tyler Moulton

Numerade Educator

Problem 29

How many significant figures are in each of the following numbers?
a) 4.01
c) 4
e) 0.00001
g) $7.01 \cdot 3.1415$
b) 4.010
d) 2.00001
f) $2.1-1.10042$

Tyler Moulton

Numerade Educator

Problem 30

Two different forces, acting on the same object, are measured. One force is $2.0031 \mathrm{~N}$ and the other force, in the same direction, is $3.12 \mathrm{~N}$. These are the only forces acting on the object. Find the total force on the object to the correct number of significant figures.

Surendra Kumar

Numerade Educator

Problem 31

Three quantities, the results of measurements, are to be added. They are $2.0600,3.163,$ and $1.12 .$ What is their sum to the correct number of significant figures?

Surendra Kumar

Numerade Educator

Problem 32

Given the equation $w=x y z,$ and $x=1.1 \cdot 10^{3}$, $y=2.48 \cdot 10^{-2},$ and $z=6.000,$ what is $w,$ in scientific notation and with the correct number of significant figures?

Tyler Moulton

Numerade Educator

Problem 33

Write this quantity in scientific notation: one tenmillionth of a centimeter

Surendra Kumar

Numerade Educator

Problem 34

Write this number in scientific notation: one hundred fifty-three million.

Tyler Moulton

Numerade Educator

Problem 35

How many inches are in 30.7484 miles?

Tyler Moulton

Numerade Educator

Problem 36

What metric prefixes correspond to the following powers of $10 ?$
a) $10^{3}$
b) $10^{-2}$
c) $10^{-3}$

Tyler Moulton

Numerade Educator

Problem 37

How many millimeters in a kilometer?

Tyler Moulton

Numerade Educator

Problem 38

A hectare is a hundred ares and an are is a hundred square meters. How many hectares are there in a square kilometer?

Tyler Moulton

Numerade Educator

Problem 39

The unit of pressure in the SI system is the pascal. What would be the SI name for 1 one-thousandth of a pascal?

Averell Hause

Carnegie Mellon University

Problem 40

The masses of four sugar cubes are measured to be $25.3 \mathrm{~g}, 24.7 \mathrm{~g}, 26.0 \mathrm{~g},$ and $25.8 \mathrm{~g} .$ Express the answers to the
following questions in scientific notation, with standard SI units and an appropriate number of significant figures.
a) If the four sugar cubes were crushed and all the sugar collected, what would be the total mass, in kilograms, of the sugar?
b) What is the average mass, in kilograms, of these four sugar cubes?

Tyler Moulton

Numerade Educator

Problem 41

What is the surface area of a right cylinder of height $20.5 \mathrm{~cm}$ and radius $11.9 \mathrm{~cm} ?$

Tyler Moulton

Numerade Educator

Problem 42

You step on your brand-new digital bathroom scale, and it reads 125.4 pounds. What is your mass in kilograms?

Tyler Moulton

Numerade Educator

Problem 43

The distance from the center of the Moon to the center of the Earth ranges from approximately $356,000 \mathrm{~km}$ to $407,000 \mathrm{~km}$. What are these distances in miles? Be certain to round your answers to the appropriate number of significant figures.

Averell Hause

Carnegie Mellon University

Problem 44

In Major League baseball, the pitcher delivers his pitches from a distance of 60 feet, 6 inches from home plate. What is the distance in meters?

Tyler Moulton

Numerade Educator

Problem 45

A flea hops in a straight path along a meter stick, starting at $0.7 \mathrm{~cm}$ and making successive jumps, which are measured to be $3.2 \mathrm{~cm}, 6.5 \mathrm{~cm}, 8.3 \mathrm{~cm}, 10.0 \mathrm{~cm}, 11.5 \mathrm{~cm}$
and $15.5 \mathrm{~cm} .$ Express the answers to the following questions in scientific notation, with units of meters and an appropriate number of significant figures. What is the total distance covered by the flea in these six hops? What is the average distance covered by the flea in a single hop?

Tyler Moulton

Numerade Educator

Problem 46

One cubic centimeter of water has a mass of 1 gram. A milliliter is equal to a cubic centimeter. What is the mass, in kilograms, of a liter of water? A metric ton is a thousand kilograms. How many cubic centimeters of water are in a metric ton of water? If a metric ton of water were held in a thin-walled cubical tank, how long (in meters) would each side of the tank be?

Tyler Moulton

Numerade Educator

Problem 47

The speed limit on a particular stretch of road is 45 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is $\frac{1}{8}$ mile, and a fortnight is a period of 2 weeks. (A microfortnight is in fact used as a unit in a particular type of computing system called the VMS system.)

Averell Hause

Carnegie Mellon University

Problem 48

According to one mnemonic rhyme, "A pint's a pound, the world around." Investigate this statement of equivalence by calculating the weight of a pint of water, assuming that the density of water is $1000 . \mathrm{kg} / \mathrm{m}^{3}$ and that the weight of $1.00 \mathrm{~kg}$ of a substance is 2.21 pounds. The volume of 1.00 fluid ounce is $29.6 \mathrm{~mL}$.

Tyler Moulton

Numerade Educator

Problem 49

If the radius of a planet is larger than that of Earth by a factor of 8.7 , how much bigger is the surface area of the planet than Earth's?

Tyler Moulton

Numerade Educator

Problem 50

If the radius of a planet is larger than that of Earth by a factor of 5.8 , how much bigger is the volume of the planet than Earth's?

Chasen Shaw

Numerade Educator

Problem 51

How many cubic inches are in 1.56 barrels?

Averell Hause

Carnegie Mellon University

Problem 52

A car's gasoline tank has the shape of a right rectangular box with a square base whose sides measure $62 \mathrm{~cm} .$ Its capacity is $52 \mathrm{~L}$. If the tank has only 1.5 L remaining, how deep is the gasoline in the tank, assuming the car is parked on level ground?

Tyler Moulton

Numerade Educator

Problem 53

The volume of a sphere is given by the formula $\frac{4}{3} \pi r^{3}$, where $r$ is the radius of the sphere. The average density of an object is simply the ratio of its mass to its volume. Using the numerical data found in Table $12.1,$ express the answers to the following questions in scientific notation, with SI units and an appropriate number of significant figures.
a) What is the volume of the Sun?
b) What is the volume of the Earth?
c) What is the average density of the Sun?
d) What is the average density of the Earth?

Averell Hause

Carnegie Mellon University

Problem 54

A tank is in the shape of an inverted cone, having height $h=2.5 \mathrm{~m}$ and base radius $r=0.75 \mathrm{~m} .$ If water is poured into the tank at a rate of $15 \mathrm{~L} / \mathrm{s}$, how long will it take to fill the tank?

Surendra Kumar

Numerade Educator

Problem 55

Water flows into a cubical tank at a rate of $15 \mathrm{~L} / \mathrm{s}$. If the top surface of the water in the tank is rising by $1.5 \mathrm{~cm}$ every second, what is the length of each side of the tank?

Tyler Moulton

Numerade Educator

Problem 56

The atmosphere has a weight that is, effectively, about 15 pounds for every square inch of Earth's surface. The average density of air at the Earth's surface is about $1.275 \mathrm{~kg} / \mathrm{m}^{3} .$ If the atmosphere were uniformly dense (it is not- - the density varies quite significantly with altitude), how thick would it be?

Suzanne W.

Numerade Educator

Problem 57

A position vector has a length of $40.0 \mathrm{~m}$ and is at an angle of $57.0^{\circ}$ above the $x$ -axis. Find the vector's components.

Surendra Kumar

Numerade Educator

Problem 58

In the triangle shown in the figure, the side lengths are $a=6.6 \mathrm{~cm}, b=13.7 \mathrm{~cm},$ and $c=9.2 \mathrm{~cm} .$ What is the value of
the angle $\gamma$ ?

Averell Hause

Carnegie Mellon University

Problem 59

Write the vectors $\vec{A}, \vec{B}$, and $\vec{C}$ in Cartesian coordinates.

Tyler Moulton

Numerade Educator

Problem 60

Calculate the length and direction of the vectors $\vec{A}, \vec{B},$ and $\vec{C}$

Prashant Bana

Numerade Educator

Problem 61

Add the three vectors $\vec{A},$ $\vec{B},$ and $\vec{C}$ graphically.

Tyler Moulton

Numerade Educator

Problem 62

Determine the difference vector $\vec{E}=\vec{B}-\vec{A}$ graphically.

Tyler Moulton

Numerade Educator

Problem 63

Add the three vectors $\vec{A}$ $\vec{B},$ and $\vec{C}$ using the component method, and find their sum vector $\vec{D}$.

Averell Hause

Carnegie Mellon University

Problem 64

Use the component method to determine the length of the vector $\vec{F}=\vec{C}-\vec{A}-\vec{B}$.

Tyler Moulton

Numerade Educator

Problem 65

Find the components of the vectors $\vec{A}, \vec{B}, \vec{C},$ and $\vec{D}$ where their lengths are given by $A=75.0, B=60.0, C=25.0$
$D=90.0$ and their angles are as shown in the figure. Write the vectors in terms of unit
vectors.

Averell Hause

Carnegie Mellon University

Problem 66

Use the components of the vectors from Problem 1.65 to find
a) the sum $\vec{A}+\vec{B}+\vec{C}+\vec{D}$ in terms of its components
b) the magnitude and direction of the sum $\vec{A}-\vec{B}+\vec{D}$

Tyler Moulton

Numerade Educator

Problem 67

The Bonneville Salt Flats, located in Utah near the border with Nevada, not far from interstate $I-80$, cover an area of over 30,000 acres. A race car driver on the Flats first heads north for $4.47 \mathrm{~km}$, then makes a sharp turn and heads southwest for $2.49 \mathrm{~km},$ then makes another turn and heads east for $3.59 \mathrm{~km} .$ How far is she from where she started?

Vishal Gupta

Numerade Educator

Problem 68

A map in a pirate's log gives directions to the location of a buried treasure. The starting location is an old oak tree. According to the map, the treasure's location is found by proceeding 20 paces north from the oak tree and then 30 paces northwest. At this location, an iron pin is sunk in the ground. From the iron pin, walk 10 paces south and dig. How far (in paces) from the oak tree is the spot at which digging occurs?

Tyler Moulton

Numerade Educator

Problem 69

The next page of the pirate's log contains a set of directions that differ from those on the map in Problem 1.68 . These say the treasure's location is found by proceeding 20 paces north from the old oak tree and then 30 paces northwest. After finding the iron pin, one should "walk 12 paces nor'ward and dig downward 3 paces to the treasure box." What is the vector that points from the base of the old oak tree to the treasure box? What is the length of this vector?

Tyler Moulton

Numerade Educator

Problem 70

The Earth's orbit has a radius of $1.5 \cdot 10^{11} \mathrm{~m}$, and that of Venus has a radius of $1.1 \cdot 10^{11} \mathrm{~m}$. Consider these two orbits to be perfect circles (though in reality they are ellipses with slight eccentricity). Write the direction and length of a vector from Earth to Venus (take the direction from Earth to Sun to be $0^{\circ}$ ) when Venus is at the maximum angular separation in the sky relative to the Sun.

Averell Hause

Carnegie Mellon University

Problem 71

A friend walks away from you a distance of $550 \mathrm{~m}$, and then turns (as if on a dime) an unknown angle, and walks an additional $178 \mathrm{~m}$ in the new direction. You use a laser range-finder to find out that his final distance from you is $432 \mathrm{~m} .$ What is the angle between his initial departure direction and the direction to his final location? Through what angle did he turn? (There are two possibilities.)

Paul A.

California State Polytechnic University, Pomona

Problem 72

The radius of Earth is $6378 . \mathrm{km}$. What is its circumference to three significant figures?

Tyler Moulton

Numerade Educator

Problem 73

Estimate the product of 4,308,229 and 44 to one significant figure (show your work and do not use a calculator), and express the result in standard scientific notation.

Tyler Moulton

Numerade Educator

Problem 74

Find the vector $\vec{C}$ that satisfies the equation $3 \hat{x}+6 \hat{y}$ $10 \hat{z}+\vec{C}=-7 \hat{x}+14 \hat{y}$

Averell Hause

Carnegie Mellon University

Problem 75

Sketch the vectors with the components $\vec{A}=\left(A_{x}, A_{y}\right)=$ $(30.0 \mathrm{~m},-50.0 \mathrm{~m})$ and $\vec{B}=\left(B_{x}, B_{y}\right)=(-30.0 \mathrm{~m}, 50.0 \mathrm{~m}),$ and
find the magnitudes of these vectors.

Averell Hause

Carnegie Mellon University

Problem 76

What angle does $\vec{A}=\left(A_{x}, A_{y}\right)=(30.0 \mathrm{~m},-50.0 \mathrm{~m})$ make
with the positive $x$ -axis? What angle does it make with the negative $y$ -axis?

Averell Hause

Carnegie Mellon University

Problem 77

Sketch the vectors with the components $\vec{A}=\left(A_{x}, A_{y}\right)=$ $(-30.0 \mathrm{~m},-50.0 \mathrm{~m})$ and $\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m}),$ and
find the magnitudes of these vectors.

Averell Hause

Carnegie Mellon University

Problem 78

What angle does $\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m})$ make
with the positive $x$ -axis? What angle does it make with the positive $y$ -axis?

Tyler Moulton

Numerade Educator

Problem 79

A position vector has components $x=34.6 \mathrm{~m}$ and $y=-53.5 \mathrm{~m} .$ Find the vector's length and angle with the $x$ -axis.

Tyler Moulton

Numerade Educator

Problem 80

For the planet Mars, calculate the distance around the Equator, the surface area, and the volume. The radius of Mars is $3.39 \cdot 10^{6} \mathrm{~m}$

Tyler Moulton

Numerade Educator

Problem 81

Find the magnitude and direction of each of the following vectors, which are given in terms of their $x$ - and $y$ -components: $\vec{A}=(23.0,59.0),$ and $\vec{B}=(90.0,-150.0)$

Tyler Moulton

Numerade Educator

Problem 82

Find the magnitude and direction of $-\vec{A}+\vec{B},$ where $\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)$

Tyler Moulton

Numerade Educator

Problem 83

Find the magnitude and direction of $-5 \vec{A}+\vec{B},$ where $\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)$

Tyler Moulton

Numerade Educator

Problem 84

Find the magnitude and direction of $-7 \vec{B}+3 \vec{A}$, where $\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)$

Tyler Moulton

Numerade Educator

Problem 85

Find the magnitude and direction of (a) $9 \vec{B}-3 \vec{A}$ and
(b) $-5 \vec{A}+8 \vec{B},$ where $\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)$

Tyler Moulton

Numerade Educator

Problem 86

Express the vectors $A=\left(A_{x}, A_{y}\right)=(-30.0 \mathrm{~m},-50.0 \mathrm{~m})$
and $\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m})$ by giving their magnitude and direction as measured from the positive $x$ -axis.

Averell Hause

Carnegie Mellon University

Problem 87

The force $F$ a spring exerts on you is directly proportional to the distance $x$ you stretch it beyond its resting length. Suppose that when you stretch a spring $8.00 \mathrm{~cm},$ it exerts a 200. N force on you. How much force will it exert on you if you stretch it $40.0 \mathrm{~cm} ?$

Tyler Moulton

Numerade Educator

Problem 88

The distance a freely falling object drops, starting from rest, is proportional to the square of the time it has been falling. By what factor will the distance fallen change if the time of falling is three times as long?

Tyler Moulton

Numerade Educator

Problem 89

A pilot decides to take his small plane for a Sunday afternoon excursion. He first flies north for 155.3 miles, then makes a $90^{\circ}$ turn to his right and flies on a straight line for 62.5 miles, then makes another $90^{\circ}$ turn to his right and flies 47.5 miles on a straight line.
a) How far away from his home airport is he at this point?
b) In which direction does he need to fly from this point on to make it home in a straight line?
c) What was the farthest distance he was away from the home airport during the trip?

Shareef Jackson

Shareef Jackson

Numerade Educator

Problem 90

As the photo shows, during a total eclipse, the Sun and the Moon appear to the observer to be almos
exactly the same size. The radii of the Sun and Moon are $r_{\mathrm{S}}=6.96 \cdot 10^{8} \mathrm{~m}$ and
$r_{M}=1.74 \cdot 10^{6} \mathrm{~m},$ respectivel
The distance between the Earth and the Moon is $d_{\mathrm{EM}}=3.84 \cdot 10^{8} \mathrm{~m}$
a) Determine the distance from the Earth to the Sun at the moment of the eclipse.
b) In part (a), the implicit assumption is that the distance from the observer to the Moon's center is equal to the distance between the centers of the Earth and the Moon. By how much is this assumption incorrect, if the observer of the eclipse is on the Equator at noon? (assumed observer-to-Moon distance-actual observer-toMoon distance)/(actual observer-to-Moon distance).
c) Use the corrected observer-to-Moon distance to determine a corrected distance from Earth to the Sun.

Cyra Jelle Calleja

Cyra Jelle Calleja

Numerade Educator

Problem 91

A hiker travels $1.50 \mathrm{~km}$ north and turns to a heading of $20.0^{\circ}$ north of west, traveling another $1.50 \mathrm{~km}$ along that heading. Subsequently, he then turns north again and travels another $1.50 \mathrm{~km} .$ How far is he from his original point of departure, and what is the heading relative to that initial point?

Paul A.

California State Polytechnic University, Pomona

Problem 92

Assuming that 1 mole $\left(6.02 \cdot 10^{23}\right.$ molecules) of an ideal gas has a volume of $22.4 \mathrm{~L}$ at standard temperature and pressure (STP) and that nitrogen, which makes up $80.0 \%$ of the air we breathe, is an ideal gas, how many nitrogen molecules are there in an average $0.500 \mathrm{~L}$ breath at STP?

Averell Hause

Carnegie Mellon University

Problem 93

On August 27,2003 , Mars approached as close to Earth as it will for over 50,000 years. If its angular size (the planet's radius, measured by the angle the radius subtends) on that day was measured by an astronomer to be 24.9 seconds of arc, and its radius is known to be $6784 \mathrm{~km}$, how close was the approach distance? Be sure to use an appropriate number of significant figures in your answer.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 94

A football field's length is exactly 100 yards, and its width is $53 \frac{1}{3}$ yards. A quarterback stands at the exact center of the field and throws a pass to a receiver standing at one corner of the field. Let the origin of coordinates be at the center of the football field and the $x$ -axis point along the longer side of the field, with the $y$ -direction parallel to the shorter side of the field.
a) Write the direction and length of a vector pointing from the quarterback to the receiver.
b) Consider the other three possibilities for the location of the receiver at corners of the field. Repeat part (a) for each.

Tyler Moulton

Numerade Educator

Problem 95

The circumference of the Cornell Electron Storage Ring is $768.4 \mathrm{~m}$. Express the diameter in inches, to the proper number of significant figures.

Tyler Moulton

Numerade Educator

Problem 96

Roughly $4.00 \%$ of what you exhale is carbon dioxide. Assume that $22.4 \mathrm{~L}$ is the volume of $1 \mathrm{~mole}\left(6.02 \cdot 10^{23} \mathrm{~mole}-\right.$
cules) of carbon dioxide and that you exhale $0.500 \mathrm{~L}$ per breath.
a) Estimate how many carbon dioxide molecules you breathe out each day.
b) If each mole of carbon dioxide has a mass of $44.0 \mathrm{~g}$, how many kilograms of carbon dioxide do you exhale in a year?

Paul A.

California State Polytechnic University, Pomona

Problem 97

The Earth's orbit has a radius of $1.5 \cdot 10^{11} \mathrm{~m},$ and that of Mercury has a radius of $4.6 \cdot 10^{10} \mathrm{~m} .$ Consider these orbits to be perfect circles (though in reality they are ellipses with slight eccentricity). Write down the direction and length of a vector from Earth to Mercury (take the direction from Earth to Sun to be $0^{\circ}$ ) when Mercury is at the maximum angular separation in the sky relative to the Sun.

Tyler Moulton

Numerade Educator