GLENCOE PHYSICS. Principles and Problems. Problems and Solutions Manual

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1 GLENCOE PHYSICS Principles and Problems Problems and Solutions Manual

2 GLENCOE PHYSICS Principles and Problems Student Edition Teacher Wraparound Edition Teacher Classroom Resources Transparency Package with Transparency Masters Laboratory Manual SE and TE Physics Lab and Pocket Lab Worksheets Study Guide SE and TE Chapter Assessment Tech Prep Applications Critical Thinking Reteaching Enrichment Physics Skills Supplemental Problems Problems and Solutions Manual Spanish Resources Lesson Plans with block scheduling Technology TestCheck Software (Win/Mac) MindJogger Videoquizzes Interactive Lesson Planner Interactive Teacher Edition Website at science.glencoe.com Physics for the Computer Age CD-ROM (Win/Mac) The Glencoe Science Professional Development Series Graphing Calculators in the Science Classroom Cooperative Learning in the Science Classroom Alternate Assessment in the Science Classroom Performance Assessment in the Science Classroom Lab and Safety Skills in the Science Classroom Glencoe/McGraw-Hill Copyright by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the Physics: Principles and Problems program. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio ISBN Printed in the United States of America

3 Contents To the Teacher iv Title Page 1 What is physics? Chapter Review Problems A Mathematical Toolkit Practice Problems Chapter Review Problems Describing Motion Practice Problems Chapter Review Problems Vector Addition Practice Problems Chapter Review Problems A Mathematical Model of Motion Practice Problems Chapter Review Problems Forces Practice Problems Chapter Review Problems Forces and Motion in Two Dimensions..55 Practice Problems Chapter Review Problems Universal Gravitation Practice Problems Chapter Review Problems Momentum and Its Conservation Practice Problems Chapter Review Problems Energy, Work, and Simple Machines Practice Problems Chapter Review Problems Energy Practice Problems Chapter Review Problems Thermal Energy Practice Problems Chapter Review Problems States of Matter Practice Problems Chapter Review Problems Waves and Energy Transfer Practice Problems Chapter Review Problems Sound Practice Problems Chapter Review Problems Light Practice Problems Chapter Review Problems Reflection and Refraction Practice Problems Chapter Review Problems Mirrors and Lenses Practice Problems Chapter Review Problems Diffraction and Interference of Light..165 Practice Problems Chapter Review Problems Static Electricity Practice Problems Chapter Review Problems Electric Fields Practice Problems Chapter Review Problems Current Electricity Practice Problems Chapter Review Problems Physics: Principles and Problems iii

4 23 Series and Parallel Circuits Practice Problems Chapter Review Problems Magnetic Fields Practice Problems Chapter Review Problems Electromagnetic Induction Practice Problems Chapter Review Problems Electromagnetism Practice Problems Chapter Review Problems Quantum Theory Practice Problems Chapter Review Problems The Atom Practice Problems Chapter Review Problems Solid State Electronics Practice Problems Chapter Review Problems The Nucleus Practice Problems Chapter Review Problems Nuclear Applications Practice Problems Chapter Review Problems Appendix B Extra Practice Problems Appendix D Additional Topics in Physics..331 To the Teacher The Problems and Solutions Manual is a supplement of Glencoe s Physics: Principles and Problems. The manual is a comprehensive resource of all student text problems and solutions. Practice Problems follow most Example Problems. Answers to these problems are found in the margin of the Teacher Wraparound Edition. Complete solutions to these problems are available to the student in Appendix C of the student text. Chapter Review Problem and Critical Thinking Problem answers are found in the margins of the Teacher Wraparound Edition. Each Practice Problem, Chapter Review Problem, and Critical Thinking Problem with the solution is restated in this manual. Complete solutions for the Extra Practice Problems in Appendix B, as well as solutions for the Additional Topics in Physics in Appendix D, can be found at the end of this manual. iv Physics: Principles and Problems

5 1 What is physics? No Practice Problems. Critical Thinking Problems page It has been said that a fool can ask more questions than a wise man can answer. In science, it is frequently the case that a wise man is needed to ask the right question rather than to answer it. Explain. Both asking a question and answering a question are important. Often, however, the training, experience, and imagination necessary to know just what question to ask have provided the insight necessary to find the answer. Physics: Principles and Problems Problems and Solutions Manual 1

6 2 A Mathematical Toolkit Practice Problems 2.1 The Measures of Science pages page Express the following quantities in scientific notation. a m m b m m c m m d m m 2. Express the following quantities in scientific notation. a kg kg b kg kg c kg kg d kg kg 3. Express the following quantities in scientific notation. a s s b s s c s s page Convert each of the following length measurements as directed. a. 1.1 cm to meters (1.1 cm) 10 2 m 1 1 cm m b pm to millimeters (76.2 pm) m 1 1 pm mm 1 1 m mm mm c. 2.1 km to meters (2.1 km) 10 3 m 1 1 km m d m to kilometers ( km m) m km 5. Convert each of the following mass measurements to its equivalent in kilograms. a. 147 g 1 kg g 1 k so 147 g g g kg kg b. 11 Mg 1 Mg g and 1 kg g so 11 Mg M 6 g 1 kg g g kg kg 2 Problems and Solutions Manual Physics: Principles and Problems

7 5. (continued) c µg 1 g 7.23 µg µg 1 kg g kg kg d. 478 mg 478 mg 10 3 g 1 1 mg 1 kg g kg page 22 Solve the following problems. Write your answers in scientific notation. 6. a kg kg (5 3) 10 7 kg kg b kg kg kg c kg kg kg d kg kg ( ) kg kg 7. a m m m 2 b m m m m 2 ( ) m m m 2 c m m m 2 d m m m m 2 8. a mg mg mg mg mg b mg mg mg mg mg c pg ng g g g g g d. 8.2 km m m m m page 23 Find the value of each of the following quantities. 9. a. ( m)( m) (2 4) m m 2 b. ( m)( m) (3 2) m m 2 c. ( m)( m) m m 2 d. ( m)( m) m m kg 10. a m kg/m kg/m kg b m ( 4) kg/m kg/m 3 Physics: Principles and Problems Problems and Solutions Manual 3

8 10. (continued) c m 04 s m/s m/s d m s ( 4) m/s m/s ( kg)( m) 11. a s kg m s kg m/s kg m/s The evaluation may be done in several other ways. For example ( kg)( m) s ( kg/s)( m) (0.5 kg/s)( m) kg m/s ( kg)( m) b s kg m s ( 2) kg m/s kg m/s a. ( mg)( kg) ( g)( g) g g 2 b. ( m)( km) ( m)( m) m m 2 c. ( ms)( ns) ( s)( s) s s a mg g 14. b g g kg m s kg m/s 2 ( m) ( m) ( km) ( km) m km m m m m Measurement Uncertainties pages page 27 State the number of significant digits in each measurement. 15. a m 4 b km 3 c m 2 d m 4 e m 2 f m a. 75 m ( kg)( m) ( s)( ms) 2 b m (continued) ( kg)( m) ( s)( s) 4 Problems and Solutions Manual Physics: Principles and Problems

9 c kg 4 d ml 3 e m 4 f m 3 page 28 Solve the following addition problems. 17. a cm, 7.4 cm, 0.68 cm, and 12.0 cm cm 7.4 cm 0.68 cm 12.0 cm cm 26.3 cm b. 1.6 km, 1.62 m, and 1200 cm 1.6 km 1600 m 1.62 m 1.62 m 1200 cm 12 m m 1600 m or 1.6 km Solve the following subtraction problems. 18. a g from 10.8 g 10.8 g g g 2.5 g (rounded from g) b m from 475 m 475 m m m 475 m (rounded from m) Solve the following multiplication problems. 19. a. 131 cm 2.3 cm cm 2 (the result cm 2 expressed to two significant digits. Note that the expression in the form 300 cm 2 would not indicate how many of the digits are significant.) b km 4.23 km 13.6 km 2 (the result km 2 expressed to three significant digits) c N 6.20 m 35.7 N m (the result N m expressed to three significant digits) Solve the following division problems. 20. a cm 7.41 s 2.73 cm/s (the result cm/s expressed to three significant digits) b cm 12.4 s cm/s (the result cm/s expressed to three significant digits) c g 11.3 mg g g g (the result g expressed to three significant digits) d g 4.4 cm g/cm 3 (the result g/cm 3 expressed to two significant digits) 2.3 Visualizing Data pages page The total distance a lab cart travels during specified lengths of time is given in the following data table. 21. (continued) Physics: Principles and Problems Problems and Solutions Manual 5

10 Distance (m) a. Plot distance versus time from the values given in the table and draw the curve that best fits all points. b. Describe the resulting curve. straight line c. According to the graph, what type of relationship exists between the total distance traveled by the lab cart and the time? linear relationship d. What is the slope of this graph? M y x m/s e. Write an equation relating distance and time for this data. d 0.30(t ) Chapter Review Problems pages page 39 Section 2.1 TABLE 2-4 Time (s) Distance (m) Time (s) Level Express the following numbers in scientific notation: a m m b m m c m m d m m 31. Convert each of the following measurements to meters. a cm 42.3 cm 10 2 m cm m b. 6.2 pm 6.2 pm m 1 pm m c. 21 km 21 km m 1 km m d mm mm 10 3 m mm m e. 214 µm 214 µm m 1 µ m m f. 570 nm 570 nm 10 9 m 1 1 nm m 32. Add or subtract as indicated. a s s s s s 32. (continued) b m m m c kg kg 6 Problems and Solutions Manual Physics: Principles and Problems

11 kg kg d g g g g g Level Rank the following mass measurements from smallest to largest: 11.6 mg, 1021 µg, kg, 0.31 mg mg 10 3 g mg g or g µg 10 6 g µ g g kg 03 g kg g 0.31 mg 10 3 g mg g or g 0.31 mg, 1021 µg, kg, 11.6 mg Section 2.2 Level State the number of significant digits in each of the following measurements. a m 1 b fm 4 c m 5 d µg State the number of significant digits in each of the following measurements. a kg 3 b kg 1 c m Add or subtract as indicated. a m m m 16.2 m m m m 34.7 m b m m m m m m m m c cm cm cm cm cm cm 2 d kg 12.0 kg kg 12.0 kg 3.07 kg 3.1 kg 37. Multiply or divide as indicated. a. ( m)( m) m m 2 7 b m s m/s c. ( km)( km) 37. (continued) km km 2 Physics: Principles and Problems Problems and Solutions Manual 7

12 kg d m kg/m kg/m Using a calculator, Chris obtained the following results. Give the answer to each operation using the correct number of significant digits. a mm 2.1 mm mm 7.4 mm b m 3.65 m m m 2 c kg kg kg 70.4 kg page A rectangular floor has a length of m and a width of 4.40 m. Calculate the area of the floor. Area lw (15.72 m)(4.40 m) m m A water tank has a mass of 3.64 kg when it is empty and a mass of 51.8 kg when it is filled to a certain level. What is the mass of the water in the tank? 51.8 kg 3.64 kg kg 48.2 kg Level A lawn is m long and 17.6 m wide. a. What length of fence must be purchased to enclose the entire lawn? Perimeter 2l 2w 2(33.21 m) 2(17.6 m) m 35.2 m m m b. What area must be covered if the lawn is to be fertilized? Area lw (33.21 m)(17.6 m) m m The length of a room is m, its width is 4.5 m, and its height is 3.26 m. What volume does the room enclose? V lwh (16.40 m)(4.5 m)(3.26 m) m m The sides of a quadrangular plot of land are m, 48.3 m, m, and m. What is the perimeter of the plot? Section 2.3 Perimeter m 48.3 m m m m m Level Figure 2 14 shows the mass of the three substances for volumes between 0 and 60 cm 3. Mass (g) (continued) Mass Versus Volume Volume (cm 3 ) 8 Problems and Solutions Manual Physics: Principles and Problems

13 a. What is the mass of 30 cm 3 of each substance? (a) 80 g, (b) 260 g, (c) 400 g. b. If you had 100 g of each substance, what would their volumes be? (a) 34 cm 3, (b) 11 cm 3, (c) 7 cm 3. c. In one or two sentences, describe the meaning of the steepness of the lines in this graph. The steepness represents the increased mass of each additional cubic centimeter of the substance. Level During an experiment, a student measured the mass of 10.0 cm 3 of alcohol. The student then measured the mass of 20.0 cm 3 of alcohol. In this way, the data in Table 2 5 were collected. relating the volume to the mass of alcohol. m V d, where m is the slope d. Find the units of the slope of the graph. What is the name given to this quantity? d m V g so the units of m are cm 3 g/cm 3 ; density 46. During a class demonstration, a physics instructor placed a 1.0-kg mass on a horizontal table that was nearly frictionless. The instructor then applied various horizontal forces to the mass and measured the rate at which it gained speed (was accelerated) for each force applied. The results of the experiment are shown in Table 2 6. Volume (cm 3 ) a. Plot the values given in the table and draw the curve that best fits all points. b. Describe the resulting curve. Mass (g) M 0 V Volume (cm 3 ) a straight line TABLE 2-5 Mass (g) c. Use the graph to write an equation page 41 a. Plot the values given in the table and draw the curve that best fits the results. Acceleration (m/s 2 ) a TABLE 2-6 Force (N) Acceleration (m/s 2 ) af Volume (cm 3 ) F Physics: Principles and Problems Problems and Solutions Manual 9

14 46. (continued) b. Describe, in words, the relationship between force and acceleration according to the graph. The acceleration varies directly with the force. c. Write the equation relating the force and the acceleration that results from the graph. F ma, where m is the slope d. Find the units of the slope of the graph. a (m/s 2 ) m so the units of m are F N m (s 2 N) 47. The physics instructor who performed the experiment in problem 46 changed the procedure. The mass was varied while the force was kept constant. The acceleration of each mass was recorded. The results of the experiment are shown in Table 2 7. a. Plot the values given in the table and draw the curve that best fits all points. Acceleration (m/s 2 ) a TABLE 2-7 Mass (kg) Acceleration (m/s 2 ) a 12 m m b. Describe the resulting curve. hyperbola c. According to the graph, what is the relationship between mass and the acceleration produced by a constant force? Acceleration varies inversely with the mass. d. Write the equation relating acceleration to mass given by the data in the graph. a m c c constant 12 m mass e. Find the units of the constant in the equation. c ma so the units of c are (kg)(m/s 2 ) kg m/s 2 Critical Thinking Problems 48. Find the approximate time needed for a pitched baseball to reach home plate. Report your result to one significant digit. (Use a reference source to find the distance thrown and the speed of a fastball.) Answers will vary with the data available. Answer should be calculated from the equation: time distance speed. 49. Have a student walk across the front of the classroom. Estimate his or her walking speed. Estimates will vary. Answers should be calculated from speed distance time 50. How high can you throw a ball? Find a tall building whose height you can estimate and compare the height of your throw to that of the building. Estimates will vary. 10 Problems and Solutions Manual Physics: Principles and Problems

15 51. Use a graphing calculator or computer graphing program to graph reaction and braking distances versus original speed. Use the calculator or computer to find the slope of the reaction distance and the best quadratic fit to the braking distance. Reaction Distance (m) Original Speed (m/s) 52. If the sun suddenly ceased to shine, how long would it take Earth to become dark? You will have to look up the speed of light in a vacuum and the distance from the sun to Earth. How long would it take to become dark on the surface of Jupiter? Speed of light m/s Mean distance from the sun to Earth m Mean distance from the sun to Jupiter m time d istance speed time for Earth to become dark: m s m/s time for the surface of Jupiter to become dark: m s m/s Braking Distance (m) Original Speed (m/s) Physics: Principles and Problems Problems and Solutions Manual 11

16 3 Describing Motion Practice Problems 3.1 Picturing Motion pages No practice problems. 3.2 Where and When? pages No practice problems. 3.3 Velocity and Acceleration pages No practice problems. Chapter Review Problems page 61 Create pictorial and physical models for the following problems. Section 3.3 Level A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go? v 0 0 m/s v m/s d 0 0 m d 1? t 0 0 s t 1 4 s Begin 19. A student drops a ball from a window 3.5 m above the sidewalk. The ball accelerates at 9.80 m/s 2. How fast is it moving when it hits the sidewalk? d m d 1 0 v 0 0 v 1? a 9.80 m/s 2 a v v v v v v v a Begin d 0 End v m/s v m/s d 0 0 m d 1? t 0 0 s t 1 5 s Begin v v v v v a0 End d 0 d 1 v 0 End Level A bike first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, then continues at this constant speed for another 4.5 s. What is the total distance traveled by the bike? t 0 0 t s t s 4.5 s d A bike accelerates from 0.0 m/s to 4.0 m/s in 4 s. What distance does it travel? 9.0 s v v m/s v m/s d 0 0 d 2? 12 Problems and Solutions Manual Physics: Principles and Problems

17 Begin Middle End 0 d 0 a 01 d 1 d 2 v v v v a A car is traveling 20 m/s when the driver sees a child standing in the road. He takes 0.8 s to react, then steps on the brakes and slows at 7.0 m/s 2. How far does the car go before it stops? a 01 0 a m/s 2 v 0 20 m/s v 1 20 m/s v 2 0 t 0 0 t s t 2? d 2? 23. If you throw the ball in problem 22 up instead of down, how fast is it moving when it hits the sidewalk? Hint: Its acceleration is the same whether it is moving up or down. d m d 1 0 m v m/s v 1? a 9.80 m/s 2 a v v v v v v Begin d 0 Begin Middle End d 0 d 1 d 2 v End v v v v v 0 d 1 a 01 0 a m/s You throw a ball downward from a window at a speed of 2.0 m/s. The ball accelerates at 9.80 m/s 2. How fast is it moving when it hits the sidewalk 2.5 m below? d m d 1 0 m v m/s v 1? a 9.80 m/s 2 a v v v v 0 Begin d 0 End d 1 Critical Thinking Problems Each of the following problems involves two objects. Draw the pictorial and physical models for each. Use different symbols to represent the position, velocity, and acceleration of each object. Do not solve the problem. 24. A truck is stopped at a stoplight. When the light turns green, it accelerates at 2.5 m/s 2. At the same instant, a car passes the truck going 15 m/s. Where and when does the truck catch up with the car? Begin End d 0 0 v 0 15 m/s a0 d 1? D 0 0 V 0 0 A2.5 m/s 2 d 1 D 1? car truck v V V v V v A V v V v The lowercase symbols represent the car s position, velocity, and accleration. The uppercase symbols represent the truck s position, velocity, and acceleration. Physics: Principles and Problems Problems and Solutions Manual 13

18 25. A truck is traveling at 18 m/s to the north. The driver of a car, 500 m to the north and traveling south at 24 m/s, puts on the brakes and slows at 3.5 m/s 2. Where do they meet? Begin End Begin D 0 0 D 1 d 1? d m V 0 18 m/s a3.5 m/s 2 v 0 24 m/s truck V V V v v v car a The lowercase symbols represent the car s position, velocity, and accleration. The uppercase symbols represent the truck s position, velocity, and acceleration. 14 Problems and Solutions Manual Physics: Principles and Problems

19 4 Vector Addition Practice Problems 4.1 Properties of Vectors pages page A car is driven 125 km due west, then 65 km due south. What is the magnitude of its displacement? 65 km south R 2 A 2 + B 2 R 2 (65 km) 2 + (125 km) 2 R km 2 R 140 km 125 km west 2. A shopper walks from the door of the mall to her car 250 m down a lane of cars, then turns 90 to the right and walks an additional 60 m. What is the magnitude of the displacement of her car from the mall door? R 2 (250 m) 2 + (60 m) 2 R m 2 Resultant140 km 250 m Resultant300 m R 260 m, or 300 m to one significant digit 3. A hiker walks 4.5 km in one direction, then makes a 45 turn to the right and walks another 6.4 km. What is the magnitude of her displacement? R 2 A 2 B 2 2AB cos 60 m 4.5 km Resultant km R [(4.5 km) 2 (6.4 km) 2 (2)(4.5 km)(6.4 km)(cos 135 )] 1/2 R km 4. What is the magnitude of your displacement when you follow directions that tell you to walk 225 m in one direction, make a 90 turn to the left and walk 350 m, then make a 30 turn to the right and walk 125 m? 225 m t 1 R 1 [(225 m) 2 (350 m) 2 ] 1/2 416 m 1 tan m m ( ) R 2 [(416 m) 2 (125 m) 2 2(416 m)(125 m) (cos )] 1/2 R m 135 R m km m page A car moving east at 45 km/h turns and travels west at 30 km/h. What are the magnitude and direction of the change in velocity? R 2 t 2 Physics: Principles and Problems Vector Addition 15

20 5. (continued) Magnitude of change in velocity 45 ( 30) 75 km/h direction of change is from east to west 6. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the front of the bus at 4.0 m/s relative to the bus. What is your speed relative to the street? 2.0 m/s 4.0 m/s 6.0 m/s relative to street 7. A motorboat heads due east at 11 m/s relative to the water across a river that flows due north at 5.0 m/s. What is the velocity of the motorboat with respect to the shore? v result v r 5.0 m/s 9. An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h to the east relative to the ground. What is the plane s speed with respect to the ground? v p 150 km/h v [v p 2 + v w 2 ] 1/2 [(150 km/h) 2 (75 km/h) 2 ] 1/2 170 km/h v w 75 km/h 10. An airplane flies due west at 185 km/h with respect to the air. There is a wind blowing at 85 km/h to the northeast relative to the ground. What is the plane s speed with respect to the ground? v v b 11 m/s v result [v 2 b v 2 r ] 1/2 [(11 m/s) 2 (5.0 m/s) 2 ] 1/2 12 m/s tan m/ s m/ s v result 12 m/s, 66 east of north 8. A boat is rowed directly upriver at a speed of 2.5 m/s relative to the water. Viewers on the shore find that it is moving at only 0.5 m/s relative to the shore. What is the speed of the river? Is it moving with or against the boat? 2.5 m/s boat 2.0 m/s river 0.5 m/s Resultant 2.5 m/s 0.5 m/s 2.0 m/s against the boat v w 85 km/h 45 v p 185 km/h v [v 2 p v 2 w 2v p v w cos ] 1/2 [(185 km/h) 2 (85 km/h) 2 (2)(185 km/h)(85 km/h)(cos 45 )] 1/2 140 km/h 4.2 Components of Vectors pages page What are the components of a vector of magnitude 1.5 m at an angle of 35 from the positive x-axis? d y y d1.5 m 35 d x v x 16 Problems and Solutions Manual Physics: Principles and Problems

21 11. (continued) d x 1.5 m cos m d y 1.5 m sin m 12. A hiker walks 14.7 km at an angle 35 south of east. Find the east and north components of this walk. d N N 35 d E 14.7 km E page A powerboat heads due northwest at 13 m/s with respect to the water across a river that flows due north at 5.0 m/s. What is the velocity (both magnitude and direction) of the motorboat with respect to the shore? v r 5.0 m/s v R N d E 14.7 km cos km d N 14.7 km sin km 13. An airplane flies at 65 m/s in the direction 149 counterclockwise from east. What are the east and north components of the plane s velocity? v N 65 m/s v E 31 v E 65 m/s cos m/s 56 m/s v N 65 m/s sin m/s 33 m/s 14. A golf ball, hit from the tee, travels 325 m in a direction 25 south of the east axis. What are the east and north components of its displacement? N m d E 325 m cos m d N 325 m sin m N E E 45 v bw (13 m/s) cos m/s v bn (13 m/s) sin m/s v RN 5.0 m/s, v rw 0.0 v RW 9.2 m/s m/s v RN 9.2 m/s 5.0 m/s 14.2 m/s v R [(9.2 m/s) 2 (14.2 m/s) 2 ] 1/2 17 m/s tan m/s tan m/s 33 v R 17 m/s, 33 west of north 16. An airplane flies due south at 175 km/h with respect to the air. There is a wind blowing at 85 km/h to the east relative to the ground. What are the plane s speed and direction with respect to the ground? 175 km/h v b 13 m/s N t t 85 km/h v R E E Physics: Principles and Problems Problems and Solutions Manual 17

22 16. (continued) v R [(175 km/h) 2 (85 km/h) 2 ] 1/2 N 190 km/h v R tan km/h tan km/h v p v R 190 km/h, 64 south of east 17. An airplane flies due north at 235 km/h with respect to the air. There is a wind blowing at 65 km/h to the northeast with respect to the ground. What are the plane s speed and direction with respect to the ground? 285 km/h t 95 km/h v we 30 v w E N t R 235 km/h To travel north, the east components must be equal and opposite. v pe v we 95 km/h cos km/h cos 1 82 km/h km/h v pn 285 km/h sin km/h v wn 95 km/h sin km/h v RN 273 km/h 47.5 km/h 320 km/h v R 320 km/h north v wn v we v wn 65 km/h sin km/h v we 65 km/h cos km/h R N 46 km/h 235 km/h 281 km/h R E 46 km/h R [(281 km/h) 2 (46 km/h) 2 ] 1/2 280 km/h tan 1 46 km/h 2 81 km/h 65 km/h 9.3 east of north 18. An airplane has a speed of 285 km/h with respect to the air. There is a wind blowing at 95 km/h at 30 north of east with respect to Earth. In which direction should the plane head in order to land at an airport due north of its present location? What would be the plane s speed with respect to the ground? E Chapter Review Problems pages page 78 Section 4.1 Level A car moves 65 km due east, then 45 km due west. What is its total displacement? d 65 km 45 km 65 km 45 km 20 km d km, east 18 Problems and Solutions Manual Physics: Principles and Problems

8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight

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