Introduction to Vectors

Introduction to Vectors 1. Which of the following natural phenomena would serve as the best time standard? a. The mean orbit radius of the earth. b. The period of audible sound waves. c. The time for one inhalation or ehalation. d. The time it takes a leaf to fall from a tree to the ground. e. The speed of the Mississippi River.. Using the prefies given in Table 1.4 of our tet, how would ou epress 4 10 9 a. 4 Gg b. 4 Tg c. 4 mg d. 4 ng e. 4 cg g? 3. If m=ρ V, where ρ is a constant of proportionalit, the kg is the unit of m, and the m 3 is the unit of V, what is the unit of ρ? a. kg m 3 b. kg c. m 3 d. kg m 3 3 e. m kg 4. If = 1 at, with meters the units of, and seconds the units of t, what are the units of a? a. m b. s c. ms d. s m e. m s 1

Introduction and Vectors 5. ssuming that m and t have different dimensions, which of the following would be phsicall meaningful? a. mt b. m+ t c. m t d. m + t m mt e. m t 6. If the mass densit of a 3 10 6 kg mass is 10 4 kg m 3, what volume in m 3 does the mass occup to the nearest order of magnitude? a. 10 1 b. 10 c. 10 3 d. 10 4 e. 10 5 7. What is the order of magnitude of the age of a 40-ear-old person in seconds? a. 10 5 b. 10 6 c. 10 7 d. 10 8 e. 10 9 8. woman walks 00 m west, then 300 m north, then 00 m south, then 00 m east. What is her displacement? a. 100 m E b. 100 m W c. 100 m N d. 100 m S e. The displacement is zero. 9. car traveled 300 km west, then 50 km south, then 150 km east, then 50 km north. What distance did it travel in km? a. 950 b. 850 c. 150 d. 50 e. 300

Chapter 1 3 10. The magnitude of vector is 3 m and that of vector is 4 m. What is the largest magnitude in meters that their sum ma have? a. 5 b. 6 c. 7 d. 8 e. 9 11. The magnitude of vector is 3 m and that of vector is 4 m. What is the smallest magnitude in meters that their sum ma have? a. 1 b. c. 3 d. 4 e. 5 1. The magnitude of vector is 3 m and that of vector is 4 m. What is the largest magnitude in meters that their difference ma have? a. 5 b. 6 c. 7 d. 8 e. 9 13. The magnitude of vector is 3 m and that of vector is 4 m. What is the smallest magnitude in meters that their difference ma have? a. 1 b. c. 3 d. 4 e. 5

4 Introduction and Vectors 14. Given the vectors below, which vector has negative components in both the and directions? a. b. c. d. e. 15. Given the vectors below, which vector has a negative component in the direction and a positive component in the direction? a. b. c. d. e.

Chapter 1 5 16. In which diagram does the sum + of the vectors and have a positive component in the direction? a. b. c. d. e. 17. In which diagram does the difference of the vectors and have a negative component in the direction? a. b. c. d. e.

6 Introduction and Vectors 18. Given the vectors below, which vector has a zero component in the direction? a. b. c. d. e. 19. Which of the following is a scalar? a. Displacement b. Force c. Velocit d. cceleration e. Distance 0. Which of the following is a vector? a. Momentum b. Temperature c. Volume d. Mass e. Densit

Chapter 1 7 1. Two vectors are shown in each diagram below. In which diagram is the sum of the two vectors equal to zero? a. b. c. d. e.. woman starts from the origin and walks 50 m west. Then she walks 15 m east. What is her displacement? a. 15 m W b. 35 m W c. 50 m W d. 65 m W e. 75 m E 3. scuba diver dives at an angle of 60 with the horizontal and swims 30 m to the top of a reef. How far under water in meters is the top of the reef? a. 15 b. 6 c. 4 d. 18 e. 1

8 Introduction and Vectors 4. woman starts at the origin and walks 9 m along the -ais. She then turns 90 and walks parallel to the - ais for 1 m. How far in meters is she from the origin? a. 9 b. 1 c. 15 d. 18 e. 1 5. What is the densit in kg m 3 of a solid cube that measures 0.700 m on a side and has a mass of 343 kg? a. 100 b. 80 c. 490 d. 1000 e. 1530 6. What is the mass in kilograms of two liters of helium, where 1. 00 " = 1. 00 10 3 cm 3 3? ρ He = 0179. kg m a. 3. 58 10 6 b. 3. 58 10 4 c. 358. 10 3 d. 8. 65 10 e. 86.5 7. If T = π ", where T is measured in seconds and " is measured in meters, what are the units of g? g a. ms b. s m c. kg s d. s kg e. 1 s

Chapter 1 9 8. If K = 1 mv, where m is measured in kilograms and v in m s, what are the units of K? a. s kg b. m s c. kg s m d. kg m s s e. kg m 9. light ear is the distance light travels in a ear. If the speed of light is c = 300. 10 8 m s, how man meters are there in a light ear? Use 365 das/ear, 4 hours/da, 60 minutes/hour, 60 seconds/minute and.54 cm/inch. a. 1. 58 10 15 b. 3. 94 10 14 c. 8. 3 10 14 d. 3. 7 10 15 e. 9. 46 10 15 30. 1.00 cubic foot of water spills on a floor. It covers 5. 8 ft. How deep is the water in centimeters? a..34 b. 1.18 c. 0.046 d. 0.178 e. 0.93 31. If an average human heart beats 70 times per minute, the best estimate of the number of times a heart will beat in 80 ears is: a. 10 5 b. 10 6 c. 10 7 d. 10 8 e. 10 9

10 Introduction and Vectors 3. Suppose that the average number of books each student carries is and that one of the states of the United States has ten percent of the 100 million students in the countr. How man books are being carried in the state in question? a. 10 6 b. 10 8 c. 10 10 d. 10 7 e. 10 9 33. What is the area in cm of a computer disk whose diameter is 5.5 inches? a. 1.6 b. 55.0 c. 140. d. 87 e. 54.9 34. Four of the products below give conversions from miles per hour to cm per second that are dimensionall or numericall incorrect. Which one is correct? 70 580 54 1 a. mi f. cm 1 h min h mi f 60 min 60 s 70 580 54 1 b. mi in. cm 100 cm 1 h min h mi f m 60 min 60 s 70 580 1 c. mi d h 36 in.54 cm mi 1 h d min f 60 min 600 s 70 580 54 1 d. mi in. cm 1 h min h mi in 60 min 60 s 70 580 54 1 e. mi f 1 in. cm 1 h min h mi f in 60 min 60 s 35. Two points in the plane have coordinates (1.0, 1.0) and (5.0,.0) in centimeters. What is the distance between the points in centimeters? a. 1.0 b..0 c. 3.0 d. 4.0 e. 5.0

Chapter 1 11 36. What are the polar coordinates of the point (8.0, 6.0)? a. r = 80., θ = 53 b. r = 10, θ = 37 c. r = 10, θ = 53 d. r = 65., θ = 30 e. r = 75., θ = 61 a f= F H G I K J π 37. What are the Cartesian coordinates of the point r, θ 0.,? 4 a. (1.4, 1.4) b. (.8,.8) c. (1.0, 3.0) F π πi d., HG 4 K J e. (0.0,.0) 38. If = 14 and = 13, what is r? a. 15 b. 16 c. 17 d. 18 e. 19 39. If = 1 and = 13, what is r? a. 1 b. 14 c. 16 d. 18 e. 5 40. If = 14. 0 cm and = 15. 0 cm, what is θ? a. 46.15 b. 43.0 c. 47.0 d. 48.9 e. 43.1

1 Introduction and Vectors 41. If = 1 cm and = 14 cm, what is θ? a. 50 b. 48 c. 7. d. 41 e. 6.1 4. If a vector has an component of 11 and a component of 13, what is the magnitude of this vector? a. 16 b. 17 c. 18 d. 19 e. 0 43. Three vectors are given b = i # + 3 # j, = 3 i # # j and C = # i+ # j. What is the sum of the three vectors? a. 3 # i+ # j b. # j 3i # c. # j+ 3i # d. # i+ # j e. 3 # i+ # j 44. person walks 50 m north, then 50 m west, then 5 m south. t what angle measured from the east direction would the person have had to walk to go directl to the destination reached? a. 6 b. 153 c. 63 d. 116 e. 7 45. If a = [ 15, 80 ], and b = 1 # i 16 # j, what is the magnitude of a b? a. 15 b. 35 c. 3 d. 5.0 e. 3

46. vector,, when added to the vector C = 3i# + 4# j, ields a resultant vector which is in the positive direction and has a magnitude equal to that of C. What is the magnitude of? a. 3. b. 6.3 c. 9.5 d. 18 e. 5.0 Chapter 1 13 47. If vector is added to vector, the result is 6 # i+ # j. If is subtracted from, the result is 4# i+ 7# j. What is the magnitude of? a. 5.1 b. 4.1 c. 5.4 d. 5.8 e. 8. 48. If C = [. 5 cm, 80 ], i.e., the magnitude and direction of C are.5 cm and 80 D = [ 3. 5 cm, 10 ], and $ E= D C, what is the direction of E to the nearest degree? a. 47 b. 35 c. 43 d. 34 e. 16 49. If = 1 # i 16 # j and = 4 i# + 10 # j, what is the magnitude of the vector C=? a. 4 b. c. 64 d. 90 e. 13 50. vector is added to = 6i# 8# j. The resultant vector is in the positive direction and has a magnitude equal to. What is the magnitude of? a. 11 b. 5.1 c. 7.1 d. 8.3 e. 1.

14 Introduction and Vectors 51. If = 1 # i 16 # j and = 4 i# + 10 # j, what is the direction of the vector C=? a. 49 b. 41 c. 90 d. +49 e. +1 5. If C = (10 m, 30 ) and D = (5 m, 130 ), what is the magnitude of the sum of these two vectors in meters? a. 0 b. 35 c. 15 d. 5 e. 5 53. The three forces shown act on a particle. What is the magnitude of the resultant of these three forces? 65 N 30 N 30 0 a. 7 N b. 33 N c. 36 N d. 4 N e. 105 N 54. In scientific notation with the correct number of significant figures, the correct value of the sum 5 4 37. 10 + 37. 10 is: a. 3. 599 10 4 b. 3. 599 10 4 c. 3. 599 10 5 d. 3. 599 10 5 e. 3. 600 10 5

Chapter 1 15 55. In scientific notation with the correct number of significant figures, the correct value of the difference 5 4 3. 7 10 3. 7 0 10 is: a.. 945 10 5 b.. 945 0 10 5 c.. 945 00 10 5 d.. 944 8 10 5 e.. 944 80 10 5 56. batter in a baseball game hits a home run and runs around the bases. The magnitude of her displacement when she returns to home plate is: a. 0 m. b. twice the distance from home plate to second base. c. the total distance around the bases. d. not defined unless we know the angles between the lines from base to base. e. not defined since a real game is not a phsics problem. 57. Given two non-zero vectors and such that = and =, which one of the following can never be correct? a. + = b. + = c. + =0 d. + = e. + = 58. Of the possible representations of a 100 m race given below, the one that phsicists would not usuall use is a a. mental representation. b. graphical representation. c. pictorial representation. d. theatrical representation. e. mathematical representation.

16 Introduction and Vectors 59. Which answer below has the correct units and correct number of significant figures for z when z is 8439. m 8.341 m obtained b the calculation z =? 1.1 m + 33. m a.. 767 10 m b.. 77 10 m c. 8. 10 m d.. 8 10 m e.. 77 10 m 60. The dimension of distance is length, ", and the dimension of time is time, t. What are the dimensions of flow rate for a liquid eiting a pipe, where the flow rate is the volume leaving the pipe in unit time? L" a. t b. c. d. NM O QP L" N M O t Q P L" 3 N M O t Q P L" 3 3 N M O t Q P e. " 3 t 61. The dimension of distance is length, ", and the dimension of time is time, t. What are the dimensions of g the quantit defined b, where L is the length of a pendulum and g is the acceleration of gravit, L 980. m s? L" a. NM O QP L t " O b. c. d. e. NM t QP L " N M O t Q P L 1 O NM t QP L1 NM O QP t

Chapter 1 17 6. Gold has a densit of 19. 3 10 3 kg m 3. One atomic mass of gold, 197 g, contains 6. 0 10 3 atoms. What volume in cubic meters does this 6. 0 10 3 atom mass occup? a. 1. 0 10 5 b. 10. 10 3 c. 1. 0 10 d. 3. 8 10 3 e. 38. 10 6 63. problem ma be solved more easil when alternative representations are used. The best strateg is to formulate representations in an order that assists in understanding the phsical principles involved. Of the orders given below, the one that will work best most often is: a. pictorial representation, mathematical representation, tabular representation, mental representation b. pictorial representation, mental representation, mathematical representation, tabular representation c. mathematical representation, pictorial representation, tabular representation, mental representation d. mathematical representation, tabular representation, mental representation, pictorial representation e. mental representation, pictorial representation, tabular representation, mathematical representation 64. If each frame of a motion picture film is 35 cm high, and 4 frames go b in a second, estimate how man frames are needed to show a two hour long movie. a. 1 400 b. 5 000 c. 50 000 d. 170 000 e. This cannot be determined without knowing how man reels were used. 65. scientific eplanation of an observation is provided b a. repeating the eperiment and getting the same numbers. b. describing the procedures for performing the eperiment. c. listing all the equations that were solved. d. giving definitions of the smbols used in the equations. e. combining the eperimental results with reasoning to answer the question how do we know? 66. The magnitude of the vector is written as. The magnitude + of the vector sum +, is a.. b.. c.. d.. e. 4.

18 Introduction and Vectors 67. Given two non-zero vectors, and, such that = = =, the sum + satisfies a. 0 +. b. 0< + <. c. +. d. < + <. e. 0 + 4. 68. Given two non-zero vectors, and, such that = = =, the difference satisfies a. 0. b. 0 < <. c. 0. d. 0< <. e. 0 4. 69. The population of the United States is now over 90 million people. The number of bars of soap used at home in a ear is closest to a. 10 8. b. 10 10. c. 10 1. d. 10 14. e. 10 16. 70. You find that a line to the top of a clindrical water tower makes an angle of 8 with a line to the base of the tower when ou are 100 m from the base of the tower. How tall is the tower? a. 47 m. b. 53 m. c. 88 m. d. 100 m. e. 188 m.

a f and D = a5 m, 150 71. If C = 10 m, 30 a. 37 b. 53 c. 17 d. 143 e. 150 7. n analsis model consists of a. a detailed summar of all characteristics of all parts of the sstem. b. a summar in which insignificant details have been ignored. c. a problem of the same general tpe that has been solved before. d. a view in three dimensions following engineering graphics rules. e. a combination of (a) and (d) above. f, what is the direction of the sum of these two vectors? Chapter 1 19