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Physics / University Physics 13 / Chapter 1

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics 13th Edition solutions

Author: Hugh D. Young, Roger A. Freedman
Publisher: Addison-Wesley
ISBN: 9780321675460
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Chapter 1 Problems

Chapter: 1 Problem: 1DQ

University Physics 13
Problem 1DQ How many correct experiments do we need to disprove a theory? How many do we need to prove a theory? Explain.

Chapter: 1 Problem: 1E

University Physics 13
Problem 1E Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.

Chapter: 1 Problem: 2DQ

University Physics 13
Problem 2DQ A guidebook describes the rate of climb of a mountain trail as 120 meters per kilometer. How can you express this as a number with no units?

Chapter: 1 Problem: 2E

University Physics 13
Problem 2E According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm, express this volume in cubic inches.

Chapter: 1 Problem: 3DQ

University Physics 13
Problem 3DQ Suppose you are asked to compute the tangent of 5.00 meters. Is this possible? Why or why not?

Chapter: 1 Problem: 3E

University Physics 13
Problem 3E How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)

Chapter: 1 Problem: 4DQ

University Physics 13
Problem 4DQ A highway contractor stated that in building a bridge deck he poured 250 yards of concrete. What do you think he meant?

Chapter: 1 Problem: 4E

University Physics 13
Problem 4E The density of gold is 19.3 g/cm3. What is this value in kilograms per cubic meter?

Chapter: 1 Problem: 5DQ

University Physics 13
Problem 5DQ What is your height in centimeters? What is your weight in newtons?

Chapter: 1 Problem: 5E

University Physics 13
Problem 5E The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 c

Chapter: 1 Problem: 6DQ

University Physics 13
Problem 6DQ The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms are gaining mass at an average rate of about 1 g/y (y =

Chapter: 1 Problem: 6E

University Physics 13
Problem 6E A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft2. If a lot has an area of 12.0 acres, what is its area in hectares?

Chapter: 1 Problem: 7DQ

University Physics 13
A power supply has a fixed output voltage of \(12.0 \mathrm{~V}\), but you need \(V_{\mathrm{T}}=3.0 \mathrm{~V}\) for an experiment. (a) Using the voltage divider shown in Fig. 19-66, what should \(R_2\) be if \(R_1\) is \(10.0 \Omega\) ? (b) What will the terminal voltage \(V_{\mathrm{T}}\) be if

Chapter: 1 Problem: 7E

University Physics 13
Problem 7E How many years older will you be 1.00 gigasecond from now? (Assume a 365-day year.)

Chapter: 1 Problem: 8DQ

University Physics 13
Problem 8DQ Describe how you could measure the thickness of a sheet of paper with an ordinary ruler.

Chapter: 1 Problem: 8E

University Physics 13
Problem 8E While driving in an exotic foreign land, you see a speed limit sign that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed

Chapter: 1 Problem: 9DQ

University Physics 13
Problem 9DQ The quantity ? = 3.14159 c is a number with no dimensions, since it is a ratio of two lengths. Describe two or three other geometrical or physical quantities that are dimensionless.

Chapter: 1 Problem: 9E

University Physics 13
A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If you are driving this car in Europe and want to compare its mileage with that of other European cars, express this mileage in km/L (L = liter). Use the conversion factors in Appendix E. (b) If this c

Chapter: 1 Problem: 10DQ

University Physics 13
Problem 10DQ What are the units of volume? Suppose another student tells you that a cylinder of radius ?r ?and height ?h? has volume given by ??r?3?h?. Explain why this cannot be right.

Chapter: 1 Problem: 10E

University Physics 13
Problem 10E The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s2. Use 1 ft = 30.48 cm to express this acce

Chapter: 1 Problem: 11DQ

University Physics 13
Problem 11DQ Three archers each fire four arrows at a target. Joes four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. All four of Moes arrows hit within 1 cm of a point 20 cm from the center, and

Chapter: 1 Problem: 11E

University Physics 13
Problem 11E Neptunium. In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nucle

Chapter: 1 Problem: 12DQ

University Physics 13
Problem 12DQ A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain.

Chapter: 1 Problem: 12E

University Physics 13
Problem 12E BIO (a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in g/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 75-kg adult recei

Chapter: 1 Problem: 13DQ

University Physics 13
Problem 13DQ Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum of zero? Explain.

Chapter: 1 Problem: 13E

University Physics 13
Problem 13E Figure 1.7 shows the result of unacceptable error in the stopping position of a train. (a) If a train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10 m, what is the percent error in the total distance covered? (b) Is it c

Chapter: 1 Problem: 14DQ

University Physics 13
Problem 14DQ One sometimes speaks of the direction of time, evolving from past to future. Does this mean that time is a vector quantity? Explain your reasoning.

Chapter: 1 Problem: 14E

University Physics 13
Problem 14E With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectan

Chapter: 1 Problem: 15DQ

University Physics 13
Problem 15DQ Air traffic controllers give instructions called vectors to tell airline pilots in which direction they are to fly. If these are the only instructions given, is the name vector used correctly? Why or why not?

Chapter: 1 Problem: 15E

University Physics 13
Problem 15E A useful and easy-to-remember approximate value for the number of seconds in a year is ? X 107. Determine the percent error in this approximate value. (There are 365.24 days in one year.)

Chapter: 1 Problem: 16DQ

University Physics 13
Problem 16DQ Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.

Chapter: 1 Problem: 16E

University Physics 13
Problem 16E How many gallons of gasoline are used in the United States in one day? Assume that there are two cars for every three people, that each car is driven an average of 10,000 miles per year, and that the average car gets 20 miles per gallon.

Chapter: 1 Problem: 17DQ

University Physics 13
Problem 17DQ (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is the negative of another? Why? Does your answer here contradict what you said in part (a)?

Chapter: 1 Problem: 17E

University Physics 13
Problem 17E BIO A rather ordinary middle-aged man is in the hospital for a routine checkup. The nurse writes 200 on the patients medical chart but forgets to include the units. Which of these quantities could the 200 plausibly represent? The patients (a) mass in kilogr

Chapter: 1 Problem: 18DQ

University Physics 13
Problem 18DQ If what must be true about the directions and magnitudes of and if C = A + B ? What must be true about the directions and magnitudes of and if C = 0?

Chapter: 1 Problem: 18E

University Physics 13
Problem 18E How many kernels of corn does it take to fill a 2-L soft drink bottle?

Chapter: 1 Problem: 19DQ

University Physics 13
Problem 19DQ If and are nonzero vectors, is it possible for both to be zero? Explain.

Chapter: 1 Problem: 19E

University Physics 13
Problem 19E How many words are there in this book?

Chapter: 1 Problem: 20DQ

University Physics 13
Problem 20DQ What does the scalar product of a vector with it-self, give? What about the vector product of a vector with itself?

Chapter: 1 Problem: 20E

University Physics 13
Problem 20E BIO Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? (b) What would the diameter

Chapter: 1 Problem: 21DQ

University Physics 13
Problem 21DQ Let represent any nonzero vector. Why is a unit vector, and what is its direction? If ? is the angle thamakes with the + x -axis, explain why is called the direction cosine for that axis.

Chapter: 1 Problem: 21E

University Physics 13
Problem 21E BIO How many times does a typical person blink her eyes in a lifetime?

Chapter: 1 Problem: 22DQ

University Physics 13
Problem 22DQ Which of the following are legitimate mathematical operations: In each case, give the reason for your answer.

Chapter: 1 Problem: 22E

University Physics 13
Problem 22E BIO How many times does a human heart beat during a persons lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm3 of blood with each beat.)

Chapter: 1 Problem: 23DQ

University Physics 13
Problem 23DQ Consider the vector products and Give an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors such that these two vector

Chapter: 1 Problem: 23E

University Physics 13
Problem 23E In Wagners opera ?Das Rheingold?, the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of gold is 19.3 g/cm3, and take its value to be about $10 per

Chapter: 1 Problem: 24DQ

University Physics 13
Show that, no matter what and are \(\vec{A}\) and \(\vec{B}\) are, \(\vec{A} \cdot(\vec{A} \times \vec{B})=0\). (Hint: Do not look for an elaborate mathematical proof. Rather look at the definition of the direction of the cross product.)

Chapter: 1 Problem: 24E

University Physics 13
Problem 24E You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle? ( Hint: Start by estimating the diameter of a drop of water.)

Chapter: 1 Problem: 25DQ

University Physics 13
Problem 25DQ (a) If does it necessarily follow that A = 0 or B = 0? Explain. (b) If does it necessarily follow that A = 0 or B = 0 ? Explain.

Chapter: 1 Problem: 25E

University Physics 13
Problem 25E How many pizzas are consumed each academic year by students at your school?

Chapter: 1 Problem: 26DQ

University Physics 13
Problem 26DQ If for a vector in the ?xy? -plane, does it follow that Ax = -Ay? What can you say about Ax and Ay?

Chapter: 1 Problem: 26E

University Physics 13
Problem 26E Hearing rattles from a snake, you make two rapid displacements of magnitude 1.8 m and 2.4 m. In sketches (roughly to scale), show how your two displacements might add up to give a resultant of magnitude (a) 4.2 in; (b) 0.6 m; (c) 3.0 m.

Chapter: 1 Problem: 27E

University Physics 13
Problem 27E A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.)

Chapter: 1 Problem: 28E

University Physics 13
Problem 28E For the vectors and in Fig. E1.24, use a scale drawing to find the magnitude and direction of (a) the vector sum and (b) the vector difference Use your answers to find the magnitude and direction of (c) a

Chapter: 1 Problem: 29E

University Physics 13
Problem 29E A spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45o east of south, and then 280 m at 30o east of north. After a fourth displacement, she finds herself back where she started. Use a scale drawing to deter

Chapter: 1 Problem: 30E

University Physics 13
Problem 30E Let ? be the angle that the vector makes with the + x -axis, measured counterclockwise from that axis. Find angle ? for a vector that has these components: (a) Ax = 2.00 m, Ay = - 1.00 m; (b) Ax = 2.00 m, Ay = 1.00 m; (c) Ax = - 2.00 m, Ay = 1.00 m; (

Chapter: 1 Problem: 31E

University Physics 13
Problem 31E Compute the x - and y -components of the vectors and in Fig. E1.24.

Chapter: 1 Problem: 32E

University Physics 13
Problem 32E Vector is in the direction 34.0o clockwise from the y-axis. The x-component of is Ax = - 16.0 m. (a) What is the y -component of ? (b) What is the magnitude of ?

Chapter: 1 Problem: 33E

University Physics 13
Problem 33E Vector has ?y?-component ?Ay? = +13.0 m. makes an angle of 32.0 counterclockwise from the +?y?-axis. (a) What is the ?x?-component o? (b) What is the magnitude of ?

Chapter: 1 Problem: 34E

University Physics 13
Problem 34E A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant disp

Chapter: 1 Problem: 35E

University Physics 13
Problem 35E For the vectors in Fig. E1.24, use the method of components to find the magnitude and direction of (a) the vector sum (b) the vector sum (c) the vector difference (d) the vector difference

Chapter: 1 Problem: 36E

University Physics 13
Problem 36E Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = - 8.60 cm, Ay = 5.20 cm; (b) Ax = - 9.70 m, Ay = - 2.45 m; (c) Ax = 7.75 km, Ay = - 2.70 km.

Chapter: 1 Problem: 37E

University Physics 13
Problem 37E A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that the

Chapter: 1 Problem: 39E

University Physics 13
Vector \(\overrightarrow{\boldsymbol{A}}\) is 2.80 cm long and is \(60.0^{\circ}\) above the \(x\)-axis in the first quadrant. Vector \(\overrightarrow{\boldsymbol{B}}\) is 1.90 cm long and is \(60.0^{\circ}\) below the \(x\)-axis in the fourth quadrant (Fig. E1.39). Use components to find the magnit

Chapter: 1 Problem: 40E

University Physics 13
Problem 40E In each case, find the x - and y -components of vector (a)

Chapter: 1 Problem: 41E

University Physics 13
Problem 41E Write each vector in Fig. E1.24 in terms of the unit vectors

Chapter: 1 Problem: 42E

University Physics 13
Problem 42E Given two vectors (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference and (c) find the magnitude and direction of the vector difference (d) In a vector diagram show

Chapter: 1 Problem: 43E

University Physics 13
Problem 43E (a) Write each vector in Fig. E1.39 in terms of the unit vectors (b) Use unit vectors to express vector where (c) Find the magnitude and direction of

Chapter: 1 Problem: 44E

University Physics 13
Problem 44E (a) Is the vector a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case justify your answer. (c) If where a?

Chapter: 1 Problem: 45E

University Physics 13
Problem 45E For the vectors in Fig. E1.24, find the scalar products

Chapter: 1 Problem: 46E

University Physics 13
Problem 46E (a) Find the scalar product of the vectors given in Exercise 1.38. (b) Find the angle between these two vectors.

Chapter: 1 Problem: 47E

University Physics 13
Problem 47E Find the angle between each of these pairs of vectors:

Chapter: 1 Problem: 48E

University Physics 13
Problem 48E Find the vector product (expressed in unit vectors) of the two vectors given in Exercise 1.38. What is the magnitude of the vector product?

Chapter: 1 Problem: 49E

University Physics 13
Problem 49E For the vectors in Fig. E1.28, (a) Find the magnitude and direction of the vector product (b) find the magnitude and direction of

Chapter: 1 Problem: 50E

University Physics 13
Problem 50E For the two vectors in Fig. E1.35, find the magnitude and direction of (a) the vector product (b) the vector product

Chapter: 1 Problem: 51E

University Physics 13
Problem 51E For the two vectors . In Fig E1.43, (a) find the scalar product (b) find the magnitude and direction of the vector product

Chapter: 1 Problem: 52E

University Physics 13
Problem 52E The vector A is 3.50 cm long and is directed into this pages. Vector Points from the lower right corner of this page to the upper left corner of this page. Define an appropriate right-handed coordinate system, and find the three components of the v

Chapter: 1 Problem: 53E

University Physics 13
Problem 53E Given two vectors and (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference and (c) find the magnitude of the vecto

Chapter: 1 Problem: 54P

University Physics 13
Problem 54P An acre has a length of one furlong and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat la

Chapter: 1 Problem: 55P

University Physics 13
Problem 55P An Earthlike Planet. In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earths mass. It is believed to consist of a mixture of rock and ice, similar

Chapter: 1 Problem: 56P

University Physics 13
Problem 56P The Hydrogen Maser. A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequ

Chapter: 1 Problem: 57P

University Physics 13
Problem 57P BIO Breathing Oxygen. The density of air under standard laboratory conditions is 1.29 kg/m3, and about 20% of that air consists of oxygen. Typically, people breathe about of air per breath. (a) How many grams of oxygen does a person breathe in a d

Chapter: 1 Problem: 58P

University Physics 13
Problem 58P A rectangular piece of aluminum is cm long and wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional un-certainty in the area is equal to the sum of the fractio

Chapter: 1 Problem: 59P

University Physics 13
Problem 59P As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 0.02 cm and a thickness of 0.050 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (

Chapter: 1 Problem: 60P

University Physics 13
BIO Biological tissues are typically made up of 98% water. Given that the density of water is \(1.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5 \(\mu \mathrm{m}\); (c) a honeybee.

Chapter: 1 Problem: 61P

University Physics 13
Problem 61P BIO Estimate the number of atoms in your body. (?Hint?: Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix D gives the atomic masses of different elemen

Chapter: 1 Problem: 62P

University Physics 13
Problem 62P How many dollar bills would you have to stack to reach the moon? Would that be cheaper than building and launching a spacecraft? (?Hint?: Start by folding a dollar bill to see how many thicknesses make 1.0 mm.)

Chapter: 1 Problem: 63P

University Physics 13
Problem 63P How much would it cost to paper the entire United States (including Alaska and Hawaii) with dollar bills? What would he the cost to each person in the United States?

Chapter: 1 Problem: 64P

University Physics 13
Stars in the Universe. Astronomers frequently say that there are more stars in the universe than there are grains of sand on all the beaches on the earth. (a) Given that a typical grain of sand is about 0.2 mm in diameter, estimate the number of grains of sand on all the earths beaches, and hence the

Chapter: 1 Problem: 65P

University Physics 13
Problem 65P Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0 west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of ea

Chapter: 1 Problem: 66P

University Physics 13
Problem 66P Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces shown in Fig. P1.60. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero.

Chapter: 1 Problem: 67P

University Physics 13
Problem 67P You are to program a robotic arm on an assembly line to move in the ?xy?-plane. Its first displacement is its second displacement is of magnitude 6.40 cm and direction 63.0 measured in the sense from the +?x- ? axis toward the ??? axis. The resul

Chapter: 1 Problem: 68P

University Physics 13
Problem 68P Emergency Landing. A plane leaves the airport in Galisteo and files 170 km at 68 east of north and then changes direction to fly 230 km at 48 south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a resc

Chapter: 1 Problem: 69P

University Physics 13
Problem 69P As noted in Exercise 1.26, a spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45o east of south, and then 280 m at 30o east of north. After a fourth displacement, she finds herself back where she started. U

Chapter: 1 Problem: 70P

University Physics 13
Problem 70P (a) Find the magnitude and direction of the vector that is the sum of the three vectors , , and in Fig. In a diagram, show how is formed from these three vectors. (b) Find the magnitude and direction of the vector

Chapter: 1 Problem: 71P

University Physics 13
Problem 71P A rocket fires two engines simultaneously. One produces a thrust of 480 N directly forward, while the other gives a 513-N thrust at 32.4 above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant forc

Chapter: 1 Problem: 72P

University Physics 13
Problem 72P A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, next 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point (Fig. P1.64). Find the magni

Chapter: 1 Problem: 73P

University Physics 13
Problem 73P Dislocated Shoulder. A patient with a dislocated shoulder is put into a traction apparatus as shown in Fig. The pulls and have equal magnitudes and must combine to produce an outward traction force of 5.60 N on the patients arm. How large should th

Chapter: 1 Problem: 74P

University Physics 13
Problem 74P On a training flight, a student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. P1.66). The directions are shown relative to north: 0o is north, 90o is east, 180o is south, and 270o is

Chapter: 1 Problem: 75P

University Physics 13
Problem 75P Equilibrium. We say an object is in ?equilibrium? if all the forces on it balance (add up to zero). Figure shows a beam weighing 124 N that is supported in equilibrium by a 100.0-N pull and a force F at the floor. The third force on the beam is the 124-N w

Chapter: 1 Problem: 76P

University Physics 13
Problem 76P Getting Back. An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 north of west, then 50 steps due south. Assume his steps all have equal length. (a) Sketch, roughly to scale, the three vector

Chapter: 1 Problem: 77P

University Physics 13
Problem 77P A graphic artist is creating a new logo for her companys website. In the graphics program she is using, each pixel in an image file has coordinates (?x?, y?), where the origin (0, 0) is at the upper left corner of the image, the +?x?-axis points to the

Chapter: 1 Problem: 78P

University Physics 13
Problem 78P A ship leaves the island of Guam and sails 285 km at 40.0 north of west. In which direction must it now head and how far must it sail so that its resultant displacement will be 115 km directly east of Guam?

Chapter: 1 Problem: 79P

University Physics 13
Problem 79P BIO Bones and Muscles. A physical therapy patient has a forearm that weighs 20.5 N and lifts a 112.0-N weight. These two forces are directed vertically downward. The only other significant forces on this forearm come from the biceps muscle (which acts perp

Chapter: 1 Problem: 80P

University Physics 13
Problem 80P You decide to go to your favorite neighborhood restaurant. You leave your apartment, take the elevator 10 flights down (each flight is 3.0 m), and then walk 15 m south to the apartment exit. You then proceed 0.200 km east, turn north, and walk 0.100 km to

Chapter: 1 Problem: 81P

University Physics 13
Problem 81P While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 km at 30.0 west of north, and finally walk 1.00 km at 40.0 north of east, where you find the treasure: a biography of Isaac Newton!

Chapter: 1 Problem: 82P

University Physics 13
Problem 82P A fence post is 52.0 m from where you are standing, in a direction 37.0 north of east. A second fence post is due south from you. What is the distance of the second post from you, if the distance between the two posts is 80.0 m?

Chapter: 1 Problem: 83P

University Physics 13
Problem 83P A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0o west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?

Chapter: 1 Problem: 84P

University Physics 13
Problem 84P Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 26.0 m in a direction 60.0o west of north. Jane walks 16.0 m in a direction 30.0o south of west. They then s

Chapter: 1 Problem: 85P

University Physics 13
Problem 85P John, Paul, and George are standing in a strawberry field. Paul is 14.0 m due west of John. George is 36.0 m from Paul, in a direction 37.0 south of east from Pauls location. How far is George from John? What is the direction of Georges location from that

Chapter: 1 Problem: 86P

University Physics 13
Problem 86P You are camping with Joe and Karl. Since all three of you like your privacy, you dont pitch your tents close together. Joes tent is 21.0 m from yours, in the direction 23.0o south of east. Karls tent is 32.0 m from yours, in the direction 37.0o north of eas

Chapter: 1 Problem: 87P

University Physics 13
Problem 87P Vectors have scalar product - 6.00, and their vector product has magnitude + 9.00. What is the angle between these two vectors?

Chapter: 1 Problem: 88P

University Physics 13
Problem 88P Bond Angle in Methane. In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates for which one of the C - H bonds is in the direction of an adjacent C - H bon

Chapter: 1 Problem: 89P

University Physics 13
Problem 89P Vector has magnitude 12.0 m and vector has magnitude 16.0 m. The scalar product is 90.0 m2. What is the magnitude of the vector product between these two vectors?

Chapter: 1 Problem: 90P

University Physics 13
Problem 90P When two vectors and are drawn from a common point, the angle between them is ???. (a) Using vector techniques, show that the magnitude of their vector sum is given by (b) If and have the same magnitude, for which value of ?

Chapter: 1 Problem: 91P

University Physics 13
Problem 91P A cube is placed so that one corner is at the origin and three edges are along the ?x -, y -, and ?z -axes of a coordinate system (Fig. P1.80). Use vectors to compute (a) the angle be-tween the edge along the ?z -axis (line ?ab?) and the diagonal from th

Chapter: 1 Problem: 92P

University Physics 13
Problem 92P Vector has magnitude 6.00 m and vector has magnitude 3.00 m. the vector product between these two vectors has magnitude 12.0 m2. What are the two possible values for the scalar product of these two vectors? for each value of , draw a

Chapter: 1 Problem: 93P

University Physics 13
Problem 93P The scalar product of vectors is + 48.0 m2. Vector has magnitude 9.00 m and direction 28.0o west of south. If vector has direction 39.0o south of east, what is the magnitude of .

Chapter: 1 Problem: 94P

University Physics 13
Problem 94P Obtain a unit vector perpendicular to the two vectors given in Exercise 1.41.

Chapter: 1 Problem: 95CP

University Physics 13
You are given vectors \(\vec{A}=5.0 \hat{\imath}-6.5 \hat{\jmath}\) and \(\overrightarrow{\boldsymbol{B}}=-3.5 \hat{\boldsymbol{\imath}}+7.0 \hat{\boldsymbol{j}}\). A third vector \(\overrightarrow{\boldsymbol{C}}\) lies in the xy-plane. Vector \(\overrightarrow{\boldsymbol{C}}\) is perpendicular to

Chapter: 1 Problem: 96P

University Physics 13
Problem 96P Two vectors have magnitudes A = 3.00 and B = 3.00. Their vector product is What is the angle between

Chapter: 1 Problem: 97P

University Physics 13
Later in our study of physics we will encounter quantities represented by \((\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \cdot \overrightarrow{\boldsymbol{C}}\). (a) Prove that for any three vectors \(\overrightarrow{\boldsymbol{A}}, \overrightarrow{\boldsymbol{B}}\), a

Chapter: 1 Problem: 98CP

University Physics 13
Problem 98CP The length of a rectangle is given as ?L ?l and its width as ?W ?w?. (a) Show that the uncertainty in its area ?A is ?a = ?Lw + ?lW?. Assume that the uncertainties ?l and ?w are small, so that the product ?lw is very small and you can ignore it. (b) Show tha

Chapter: 1 Problem: 99CP

University Physics 13
Completed Pass. At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at \(+1.0 \hat{\imath}-5.0 \hat{\jmath}\), where the units are y

Chapter: 1 Problem: 100CP

University Physics 13
Problem 100CP DATA ?Navigating in the Solar System. The Mars Polar Lander spacecraft was launched on January 3, 1999. On December 3, 1999, the day ?Mars Polar Lander impacted the Martian surface at high velocity and probably disintegrated, the positions of the earth a

Chapter: 1 Problem: 101CP

University Physics 13
Problem 101CP Navigating in the Big Dipper. All of the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. ?Figure P1.91 shows the distances from the earth to

Chapter: 1 Problem: 102CP

University Physics 13
Problem 102CP The vector called the ?position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (?x?, ?y?, z?). Use what you know about vectors to prove the following: All points (?x?, ?y

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