Test Bank for University Physics with Modern Physics, 14th Edition by Hugh D. Young , Roger A. Freedman

TEST BANK FOR UNIVERSITY PHYSICS WITH MODERN PHYSICS, 14TH EDITION BY HUGH D. YOUNG, ROGER A. FREEDMAN MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The current definition of the standard meter of length is based on 1) A) the length of a particular object kept in France. B) the distance between the earth's equator and north pole. C) the distance traveled by light in a vacuum. D) the distance between the earth and the sun. 2) The current definition of the standard second of time is based on 2) A) the frequency of radiation emitted by cesium atoms. B) the duration of one year. C) the earth's rotation rate. D) the oscillation of a particular pendulum kept in France. 3) The current definition of the standard kilogram of mass is based on 3) A) the mass of the earth. B) the mass a particular object kept in France. C) the mass of the sun. D) the mass of a cesium-133 atom. 4) If a woman weighs 125 lb, her mass expressed in kilograms is x kg, where x is 4) A) less than 125. B) greater than 125. 5) If a tree is 15 m tall, its height expressed in feet is x ft, where x is 5) A) less than 15. B) greater than 15. 6) If a flower is 6.5 cm wide, its width expressed in millimeters is x mm, where x is 6) A) less than 6.5. B) greater than 6.5. 7) If an operatic aria lasts for 5.75 min, its length expressed in seconds is x s, where x is 7) A) less than 5.75. B) greater than 5.75. 8) Scientists use the metric system chiefly because it is more accurate than the English system. 8) A) True B) False 9) When adding two numbers, the number of significant figures in the sum is equal to the number of significant figures in the least accurate of the numbers being added. 9) A) True B) False 10) When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted. 10) A) True B) False 1 11) Which of the following is an accurate statement? 11) A) Rotating a vector about an axis passing through the tip of the vector does not change the vector. B) The magnitude of a vector can be zero even though one of its components is not zero. C) It is possible to add a scalar quantity to a vector. D) The magnitude of a vector is independent of the coordinate system used. E) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. 12) If A - B = 0, then the vectors A and B have equal magnitudes and are directed in the opposite directions from each other. 12) A) True B) False 13) Under what condition is | A - B | = A + B? 13) A) The magnitude of vector B is zero. B) Vectors A and B are in the same direction. C) Vectors A and B are in opposite directions. D) Vectors A and B are in perpendicular directions. E) The statement is never true. 14) If A B, under what condition is | A - B | = A - B? 14) A) Vectors A and B are in opposite directions. B) Vectors A and B are in the same direction. C) Vectors A and B re in perpendicular directions. D) The statement is never true. E) The statement is always true. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 15) For the vectors shown in the figure, express vector S in terms of vectors M and N . 15) 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 16) The magnitude of a vector can never be less than the magnitude of one of its components. 16) A) True B) False 17) If the magnitude of vector A is less than the magnitude of vector B , then the x component of A is less than the x component of B . 17) A) True B) False 18) If the eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements about these two vectors is correct? 18) A) Vector A is parallel to vector B . B) The magnitude of vector A is twice the magnitude of vector B . C) Vectors A and B point in opposite directions. D) The magnitude of vector A is equal to the magnitude of vector B . E) Vector A is perpendicular to vector B . 19) If all the components of a vector are equal to 1, then that vector is a unit vector. 19) A) True B) False 20) If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. 20) A) True B) False 21) If two nonzero vectors point in the same direction, their dot product must be zero. 21) A) True B) False 22) The value of the dot product of two vectors depends on the particular coordinate system being used. 22) A) True B) False 23) If two vectors are perpendicular to each other, their cross product must be zero. 23) A) True B) False 24) If two vectors point in opposite directions, their cross product must be zero. 24) A) True B) False 3 25) If A and B are nonzero vectors for which A ∙ B = 0, it must follow that 25) A) |A × B | = AB. B) A is parallel to B . C) |A × B | = 1. D) A × B = 0. 26) Convert 1.2 × 10-3 to decimal notation. 26) A) 1.200 B) 0.1200 C) 0.0120 D) 0.0012 E) 0.00012 27) Write out the number 7.35 × 10-5 in full with a decimal point and correct number of zeros. 27) A) 0. B) 0. C) 0. D) 0.00735 E) 0.0735 28) 0. can also be expressed as 28) A) 1.776 × 10-3. B) 1.776 × 10-4. C) 17.72 × 104. D) 1772 × 105. E) 177.2 × 107. 29) 0.00325 × 10-8 cm can also be expressed in mm as 29) A) 3.25 × 10-12 mm. B) 3.25 × 10-11 mm. C) 3.25 × 10-10 mm. D) 3.25 × 10-9 mm. E) 3.25 × 10-8 mm. 30) If, in a parallel universe, π has the value 3.14149, express π in that universe to four significant figures. 30) A) 3.141 B) 3.142 C) 3.1415 D) 3.1414 31) The number 0. has 31) A) 7 significant figures. B) 6 significant figures. C) 4 significant figures. D) 2 significant figures. 32) What is 0.674 0.74 to the proper number of significant figures? 32) A) 0.91 B) 0.911 C) 0.9 D) 0.9108 4 33) What is the value of π(8.104)2, written with the correct number of significant figures? 33) A) 206.324 B) 206.323 C) 206.3 D) 206 E) 200 34) What is the sum of 1123 and 10.3 written with the correct number of significant figures? 34) A) 1.13 × 103 B) 1.1 × 103 C) 1133.3 D) 1133.3000 E) 1133 35) What is the sum of 1.53 + 2.786 + 3.3 written with the correct number of significant figures? 35) A) 8 B) 7.6 C) 7.62 D) 7.616 E) 7.6160 36) What is the difference between 103.5 and 102.24 written with the correct number of significant figures? 36) A) 1 B) 1.3 C) 1.26 D) 1.260 E) 1.2600 37) What is the product of 11.24 and 1.95 written with the correct number of significant figures? 37) A) 22 B) 21.9 C) 21.92 D) 21.918 E) 21.9180 38) What is the result of 1.58 ÷ 3.793 written with the correct number of significant figures? 38) A) 4.2 × 10-1 B) 4.1656 × 10-1 C) 4.166 × 10-1 D) 4.17 × 10-1 E) 4 × 10-1 39) What is 34 + (3) × (1.2465) written with the correct number of significant figures? 39) A) 4 × 101 B) 37.7 C) 37.74 D) 37.7395 E) 38 40) What is 56 + (32.00)/(1.2465 + 3.45) written with the correct number of significant figures? 40) A) 62.812 B) 62.8 C) 63 D) 62.81 E) 62. 5 41) Add 3685 g and 66.8 kg and express your answer in milligrams (mg). 41) A) 7.05 × 107 mg B) 7.05 × 105 mg C) 7.05 × 104 mg D) 7.05 × 106 mg 42) Express (4.3 × 106)-1/2 in scientific notation. 42) A) 2.1 × 104 B) 2.1 × 103 C) 2.1 × 10-5 D) 4.8 × 10-4 43) What is 0.2052/3, expressed to the proper number of significant figures? 43) A) 0.35 B) 0.3 C) 0.348 D) 0.3477 44) The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as 44) A) 0.7 m2. B) 0.68 m2. C) 0.682 m2. D) 0.6818 m2. E) 0.68175 m2. 45) The following exact conversion equivalents are given: 1 m = 100 cm, 1 in = 2.54 cm, and 1 ft = 12 in. If a computer screen has an area of 1.27 ft2, this area is closest to 45) A) 0.284 m2. B) 0.00284 m2. C) 4.65 m2. D) 0.0465 m2. E) 0.118 m2. 46) In addition to 1 m = 39.37 in., the following exact conversion equivalents are given: 1 mile = 5280 ft, 1 hour = 60 min, and 1 min = 60 s. If a particle has a velocity of 8.4 miles per hour, its velocity, in m/s, is closest to 46) A) 3.0 m/s. B) 4.5 m/s. C) 4.1 m/s. D) 3.4 m/s. E) 3.8 m/s. 47) A weight lifter can bench press 171 kg. How many milligrams (mg) is this? 47) A) 1.71 × 108 mg B) 1.71 × 109 mg C) 1.71 × 107 mg D) 1.71 × 106 mg 48) How many nanoseconds does it take for a computer to perform one calculation if it performs 6.7 × 107 calculations per second? 48) A) 67 ns B) 11 ns C) 15 ns D) 65 ns 6 49) The shortest wavelength of visible light is approximately 400 nm. Express this wavelength in centimeters. 49) A) 4 × 10-11 cm B) 4 × 10-5 cm C) 4 × 10-7 cm D) 4 × 10-9 cm E) 400 × 10-11 cm 50) The wavelength of a certain laser is 0.35 micrometers, where 1 micrometer = 1 × 10-6 m. Express this wavelength in nanometers. 50) A) 3.5 × 104 nm B) 3.5 × 102 nm C) 3.5 × 103 nm D) 3.5 × 101 nm 51) A certain CD-ROM disk can store approximately 6.0 × 102 megabytes of information, where 106 bytes = 1 megabyte. If an average word requires 9.0 bytes of storage, how many words can be stored on one disk? 51) A) 2.1 × 107 words B) 2.0 × 109 words C) 5.4 × 109 words D) 6.7 × 107 words 52) A plot of land contains 5.8 acres. How many square meters does it contain? [1 acre = 43,560 ft2] 52) A) 5.0 × 104 m2 B) 7.1 × 103 m2 C) 7.0 × 104 m2 D) 2.3 × 104 m2 53) A person on a diet loses 1.6 kg in a week. How many micrograms/second (μg/s) are lost? 53) A) 2.6 × 103 μg/s B) 1.6 × 105 μg/s C) 6.4 × 104 μg/s D) 44 μg/s SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 54) Albert uses as his unit of length (for walking to visit his neighbors or plowing his fields) the albert (A), the distance Albert can throw a small rock. One albert is 92 meters. How many square alberts is equal to one acre? (1 acre = 43,560 ft2 = 54) 4050 m2) 7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 55) Convert a speed of 4.50 km/h to units of ft/min. (1.00 m = 3.28 ft) 55) A) 886 ft/min B) 82.3 ft/min C) 165 ft/min D) 0.246 ft/min E) 246 ft/min 56) The exhaust fan on a typical kitchen stove pulls 600 CFM (cubic feet per minute) through the filter. Given that 1.00 in. = 2.54 cm, how many cubic meters per second does this fan pull? 56) A) 3.05 m3/sec B) 32.8 m3/sec C) 0.283 m3/sec D) 0.328 m3/sec 57) The mass of a typical adult woman is closest to 57) A) 35 kg. B) 20 kg. C) 75 kg. D) 150 kg. 58) The height of the ceiling in a typical home, apartment, or dorm room is closest to 58) A) 100 cm. B) 200 cm. C) 400 cm. D) 500 cm. 59) Approximately how many times does an average human heart beat in a year? 59) A) 4 × 105 B) 4 × 108 C) 4 × 107 D) 4 × 109 E) 4 × 106 60) Approximately how many times does an average human heart beat in a lifetime? 60) A) 3 × 1010 B) 3 × 109 C) 3 × 107 D) 3 × 108 E) 3 × 1011 61) Approximately how many pennies would you have to stack to reach an average 8-foot ceiling? 61) A) 2 × 104 B) 2 × 105 C) 2 × 103 D) 2 × 102 E) 2 × 106 62) Estimate the number of times the earth will rotate on its axis during a human's lifetime. 62) A) 3 × 105 B) 3 × 108 C) 3 × 104 D) 3 × 106 E) 3 × 107 63) Estimate the number of pennies that would fit in a box one foot long by one foot wide by one foot tall. 63) A) 5 × 103 B) 5 × 104 C) 5 × 106 D) 5 × 105 E) 5 × 102 8 64) A marathon is 26 mi and 385 yd long. Estimate how many strides would be required to run a marathon. Assume a reasonable value for the average number of feet/stride. 64) A) 4.5 × 104 strides B) 4.5 × 105 strides C) 4.5 × 103 strides D) 4.5 × 106 strides 65) The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, ℓ, what combination of g and ℓ must the period be proportional to? (Acceleration has SI units of m • s-2.) 65) A) gℓ2 B) ℓ/g C) gℓ D) gℓ E) g/ℓ 66) The speed of a wave pulse on a string depends on the tension, F, in the string and the mass per unit length, μ, of the string. Tension has SI units of kg • m • s-2 and the mass per unit length has SI units of kg • m-1. What combination of F and μ must the speed of the wave be proportional to? 66) A) F / μ B) μ / F C) F / μ D) μ / F E) μF 67) The position x, in meters, of an object is given by the equation x = A + Bt + Ct2, where t represents time in seconds. What are the SI units of A, B, and C? 67) A) m, m/s, m/s2 B) m, m, m C) m/s, m/s2, m/s3 D) m, s, s E) m, s, s2 68) You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started? 68) A) 46 m B) 50 m C) 87 m D) 94 m 9 69) Vectors A and B are shown in the figure. Vector C is given by C = B - A . The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units. What is the magnitude of vector C ? 69) A) 9.00 B) 17.5 C) 16.2 D) 9.53 E) 15.5 70) Vectors A and B are shown in the figure. Vector C is given by C = B - A . The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units. What is the angle of vector C , measured counterclockwise from the +x-axis? 70) A) 22.4° B) 292° C) 287° D) 73.1° E) 16.9° 10 71) A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit? 71) A) 10 m B) 8.8 m C) 8.1 m D) 66 m 72) You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east. 72) A) 63° N of E B) 69° N of E C) 57° N of E D) 50° N of E 73) Vector A has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector A . 73) A) Ax = 4.29 and Ay = 2.16 B) Ax = -3.21 and Ay = 3.83 C) Ax = 3.83 and Ay = 3.21 D) Ax = 3.83 and Ay = -3.21 E) Ax = -3.21 and Ay = -3.83 74) The components of vector A are A x = + 3.90 and A y = -4.00. What is the angle 74) measured counterclockwise from the +x-axis to vector A ? A) 136° B) 314° C) 224° D) 134° E) 46.0° SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 75) Vector A has a magnitude of 5.5 cm and points along the x-axis. Vector B has a magnitude of 7.5 cm and points at +30° above the negative x-axis. 75) (a) Determine the x and y components of Vector A . (b) Determine the x and y components of Vector B. (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. 11 76) Vector A has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector B has a magnitude of 25.0 cm and points along the negative x-axis. Vector C has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector A . (b) Determine the x and y components of Vector B . (c) Determine the x and y components of Vector C . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. 76) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 77) A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill? 77) A) 444 m/s B) 220 m/s C) 8.9 m/s D) 435 m/s 78) An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope? 78) A) 15 m/s B) 8.7 m/s C) 12 m/s D) 5.5 m/s 79) The components of vector A are A x = +2.2 and A y = -6.9, and the components of 79) vector B are given are B x = -6.1 and B y = -2.2. What is the magnitude of the vector B - A ? A) 6.1 B) 9.5 C) 9.9 D) 0.76 E) 91 80) The components of vector B are B x = -3.5 and B y = -9.7, and the components of 80) vector C are C x = -6 and C y = +8.1. What is the angle (less than 180 degrees) between vectors B and C ? A) 17° B) 106° C) 56° D) 124° E) 163° 81) An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point. 81) A) 78 km B) 76 km C) 79 km D) 82 km E) 81 km 12 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 82) In the figure, the magnitude of vector A is 18.0 units, and the magnitude of vector B is 12.0 units. What vector C must be added to the vectors A and B so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector C by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive. 82) 13 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 83) Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes F 1 = 1.0 83) N, F 2 = 8.0 N and F 3 = 7.0 N, where N is the standard unit of force, what is the component of the net force F net = F 1 + F 2 + F 3 parallel to the floor? A) 6.0 N B) 7.8 N C) 5.1 N D) 2.5 N 84) As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F 1 = 80.0 N, F 2 = 60.0 N, and F 3 = 40.0 N, where N 84) is the standard SI unit of force. The resultant force acting on the object is given by A) 180 N at an angle 60.0° with respect to +x-axis. B) 40.0 N at an angle 60.0° with respect to +x-axis. C) 35.5 N at an angle 34.3° with respect to +x-axis. D) 60.0 N at an angle 90.0° with respect to +x-axis. E) 20.0 N at an angle 34.3° with respect to +x-axis. 14 85) A teacher sends her students on a treasure hunt. She gives the following instructions: 1. Walk 300 m north. 2. Walk 400 m northwest. 3. Walk 700 m east-southeast and the treasure is buried there. As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk? 85) A) 187 m in a direction 67.3° north of east B) 481 m in a direction 40.9° north of east C) 284 m in a direction 28.2° west of north D) 399 m in a direction 52.5° north of east E) The treasure position cannot be reached in one straight walk. ^ ^ ^ ^ 86) Vector A = -3.00 i . What is vector C = A + B ? + 3.00 j and vector B = 3.00 i + 4.00 j 86) ^ ^ A) 7.00 i + 7.00 j ^ ^ B) -3.00 i + 7.00 j ^ ^ C) 0.00 i + 7.00 j ^ ^ D) -3.00 i - 3.00 j ^ ^ E) 0.00 i + 3.00 j ^ ^ ^ ^ 87) Vector A = 1.00 i . What are the magnitude and direction of vector C = A + B ? + -2.00 j and vector B = 3.00 i + 4.00 j 87) A) 7.21 in a direction 33.7° counterclockwise from the positive x axis B) 7.21 in a direction 56.3° counterclockwise from the positive x axis C) 4.47 in a direction 26.6° counterclockwise from the positive x axis D) 6.00 in a direction 63.4° counterclockwise from the positive x axis E) 4.47 in a direction 6.34° counterclockwise from the positive x axis ^ 88) What is the magnitude of A + B + C , where A = 1.00 i , B = 3.00 i ^ ^ + 4.00 j - 1.00 k 88) ^ ^ ^ ^ ^ - 1.00 j - 4.00 k and C = -1.00 i + 1.00 j ? A) 8.12 B) 2.00 C) 6.78 D) 7.07 E) 10.76 ^ ^ ^ ^ ^ ^ 89) If A = +4 i - 2 j - 3 k and C = -4 i -2 j - 3 k , which of the following numbers is closest 89) to the magnitude of A - C ? A) 10 B) 8 C) 11 D) 7 E) 9 15 ^ ^ ^ ^ 90) Vector A = -1.00i . What are the magnitude and direction of vector C = 3.00A + 2.00B ? + -2.00j and vector B = 3.00 i + 4.00 j 90) A) 3.61 in a direction 33.7° counterclockwise from the positive x-axis B) 3.61 in a direction -56.3° counterclockwise from the positive x-axis C) 6.72 in a direction 34.4° counterclockwise from the positive x-axis D) 3.61 in a direction 56.3° counterclockwise from the positive x-axis E) 5.00 in a direction 56.3° counterclockwise from the positive x axis 91) Vectors A and B are shown in the figure. What is -5.00 A + 4.00B ? 91) A) 34.0 B) 31.8 ^ ^ C) -2.00i - 32.0j ^ ^ D) -32.0i - 2.00j E) 1028 ^ ^ ^ 92) Determine the scalar product of A = 6.0 i ^ ^ ^ + 4.0j - 2.0k and B = 5.0i - 6.0j - 3.0k . 92) A) 60 ^ ^ ^ B) 30 i - 24j + 6k ^ ^ ^ C) 30 i + 24j + 6k D) 12 E) undefined 16 93) Determine the angle between the directions of vector A = 3.00i ^ and vector B = -3.00i ^ + 1.00j 93) ^ ^ + 3.00j . A) 88.1° B) 45.2° C) 30.0° D) 26.6° E) 117° ^ ^ 94) The scalar product of vector A = 3.00i + 2.00j and vector B is 10.0. Which of the 94) following vectors could be vector B ? ^ ^ A) 4.00i + 6.00j ^ B) 12.0i ^ ^ C) 2.00i + 2.00j ^ ^ D) 2.00i + 4.00j ^ ^ E) 5.00i + 4.00j ^ ^ 95) The angle between vector A = 2.00i + 3.00j and vector B is 45.0°. The scalar product 95) of vectors A and B is 3.00. If the x component of vector B is positive, what is vector B . ^ ^ A) 4.76i + 0.952j ^ ^ B) 1.15i + 0.231j ^ ^ C) 0.871i + 0.419j ^ ^ D) 3.42i + 0.684j ^ ^ E) 2.96i + -0.973j ^ ^ ^ 96) What is the angle between the vector A = +3i - 2j - 3k and the +y-axis? 96) A) 25° B) 90° C) 65° D) 155° E) 115° SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ^ ^ ^ ^ ^ ^ 97) If A = 3i - j + 4k and B = xi + j - 5k , find x so B will be perpendicular to A . 97) 98) Two boys searching for buried treasure are standing underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree. 98) 17 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 99) A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3) B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3) If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to: 99) A) 22.5°. B) 21.8°. C) 26.6°. D) 36.9°. E) 45.0°. 100) For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product A × C is closest to 100) A) zero. B) 16. C) -45. D) -16. E) 45. ^ ^ ^ 101) What is the vector product of A = 2.00 i ^ ^ + 3.00 j + 1.00 k and B = 1.00 i - 3.00 j - 101) ^ 2.00 k ? ^ ^ ^ A) -3.00 i + 5.00 j - 9.00 k ^ ^ ^ B) -9.00 i - 3.00 j - 3.00 k ^ ^ ^ C) -5.00 i + 2.00 j - 6.00 k ^ ^ ^ D) 2.00 i -9.00 j - 2.00 k ^ ^ ^ E) -4.00 i + 3.00 j - 1.00 k 102) What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north? 102) A) 6.93 B) -4.00 C) -6.93 D) 8.00 E) 4.00 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 103) If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors? 103) 18 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ^ ^ ^ ^ 104) If C = -4i - 2j - 3k , what is C × j ? 104) ^ ^ A) -3i + 4k ^ ^ ^ B) +3i + 2 j - 4k ^ ^ ^ C) -3i - 2 j + 4k ^ ^ D) +3i - 4k ^ ^ E) +3i + 4k ^ ^ ^ ^ ^ ^ 105) If B = -2i , which of the following numbers is closest to the magnitude of C × B ? - 6j + 2k and C = -2i -2j - 3k 105) A) 9 B) 25 C) 17 D) 13 E) 21 106) For the vectors shown in the figure, find the magnitude and direction of B × A , assuming that the quantities shown are accurate to two significant figures. 106) A) 26, directed out of the plane B) 26, directed into the plane C) 31, directed on the plane D) 31, directed into the plane E) 31, directed out of the plane 19 107) For the vectors shown in the figure, find the magnitude and direction of the vector product A × C , assuming that the quantities shown are accurate to two significant figure. 107) A) 45, directed out of the plane B) 16, directed out of the plane C) 45, directed on the plane D) 45, directed into the plane E) 16, directed into the plane 20 Answer Key Testname: UNTITLED1 1) C 2) A 3) B 4) A 5) B 6) B 7) B 8) B 9) B 10) B 11) D 12) B 13) C 14) B 15) S = M - N 16) A 17) B 18) D 19) B 20) A 21) B 22) B 23) B 24) A 25) A 26) D 27) B 28) B 29) C 30) A 31) C 32) A 33) C 34) E 35) B 36) B 37) B 38) D 39) E 40) C 41) A 42) D 43) C 44) C 45) E 46) E 47) A 48) C 49) B 21 Answer Key Testname: UNTITLED1 50) B 51) D 52) D 53) A 54) 1.29 A2 55) E 56) C 57) C 58) B 59) C 60) B 61) C 62) C 63) B 64) A 65) B 66) A 67) B 68) C 69) C 70) C 71) B 72) A 73) E 74) B 75) (a) A x = 5.5 cm, A y = 0 (b) B x = -6.5 cm, B y = 3.8 cm (c) R x = -1.0 cm, R y = 3.8 cm (d) 3.9 cm at 75° above -x-axis 76) (a) A x = 65 cm, A y = 38 cm (b) B x = -25 cm, B y = 0 (c) C x = -28 cm, C y = -28 cm (d) R x = 12 cm, R y = 9.2 cm (e) 15 cm at 38° above +x-axis 77) C 78) D 79) B 80) D 81) C 82) 15.5, 209° 83) D 84) C 85) B 86) C 87) C 88) D 22 Answer Key Testname: UNTITLED1 89) B 90) A 91) B 92) D 93) E 94) C 95) B 96) E 97) 7 98) -90 m2 99) B 100) D 101) A 102) A 103) 26.6° 104) D 105) B 106) B 107) A 23 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the acceleration of an object is negative, the object must be slowing down. 1) A) True B) False 2) If the graph of the position as a function of time for an object is a horizontal line, that object cannot be accelerating. 2) A) True B) False 3) If an object is accelerating toward a point, then it must be getting closer and closer to that point. 3) A) True B) False 4) When can we be certain that the average velocity of an object is always equal to its instantaneous velocity? 4) A) only when the acceleration is changing at a constant rate B) always C) only when the acceleration is constant D) only when the velocity is constant E) never 5) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? 5) A) In equal times it moves equal distances. B) In equal times its velocity changes by equal amounts. C) In equal times its speed changes by equal amounts. D) A graph of its velocity as a function of time is a horizontal line. E) A graph of its position as a function of time has a constant slope. 6) Suppose that a car traveling to the west (the -x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct? 6) A) Its acceleration is negative but its velocity is positive. B) Its acceleration is positive but its velocity is negative. C) Both its acceleration and its velocity are positive. D) Both its acceleration and its velocity are negative. 1 7) The motion of a particle is described in the velocity versus time graph shown in the figure. We can say that its speed 7) A) decreases. B) increases. C) decreases and then increases. D) increases and then decreases. 8) The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0. At time T, what is true about these two vehicles since time t = 0? 8) A) The car will have traveled further than the truck. B) The truck will have traveled further than the car. C) The truck and the car will have traveled the same distance. D) The car will be traveling faster than the truck. 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 9) The graph in the figure shows the position of an object as a function of time. The letters H-L represent particular moments of time. At which moments shown (H, I, etc.) is the speed of the object (a) the greatest? (b) the smallest? 9) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) The figure shows the position of an object (moving along a straight line) as a function of time. Assume two significant figures in each number. Which of the following statements about this object is true over the interval shown? 10) A) The average speed of the object is 1.0 m/s. B) The object is accelerating to the left. C) The acceleration of the object is in the same direction as its velocity. D) The object is accelerating to the right. 3 11) The figure shows the graph of the position x as a function of time for an object moving in the straight line (the x-axis). Which of the following graphs best describes the velocity along the x-axis as a function of time for this object? 11) A) B) C) 4 D) E) 12) An object is moving with constant non-zero acceleration along the +x-axis. A graph of the velocity in the x direction as a function of time for this object is 12) A) a straight line making an angle with the time axis. B) a parabolic curve. C) a vertical straight line. D) a horizontal straight line. 5 13) An object is moving in a straight line along the x-axis. A plot of its velocity in the x direction as a function of time is shown in the figure. Which graph represents its acceleration in the x direction as a function of time? 13) A) 6 B) C) 7 D) E) 8 14) An object starts its motion with a constant velocity of 2.0 m/s toward the east. After 3.0 s, the object stops for 1.0 s. The object then moves toward the west a distance of 2.0 m in 3.0 s. The object continues traveling in the same direction, but increases its speed by 1.0 m/s for the next 2.0 s. Which graph below could represent the motion of this object? 14) A) B) 9 C) D) 10 15) The figure shows the velocity of a particle as it travels along the x-axis. What is the direction of the acceleration at t = 0.5 s? 15) A) in the -x direction B) in the +x direction C) The acceleration is zero. 16) The figure represents the velocity of a particle as it travels along the x-axis. At what value (or values) of t is the instantaneous acceleration equal to zero? 16) A) t = 1 s B) t = 0 C) t = 0.5 s and t = 2 s 11 17) A ball is thrown directly upward and experiences no air resistance. Which one of the following statements about its motion is correct? 17) A) The acceleration of the ball is downward while it is traveling up and upward while it is traveling down. B) The acceleration of the ball is downward while it is traveling up and downward while it is traveling down but is zero at the highest point when the ball stops. C) The acceleration is downward during the entire time the ball is in the air. D) The acceleration of the ball is upward while it is traveling up and downward while it is traveling down. 18) Two objects are thrown from the top of a tall building and experience no appreciable air resistance. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street? 18) A) The one thrown up is traveling faster. B) They are traveling at the same speed. C) The one thrown down is traveling faster. 19) Two objects are dropped from a bridge, an interval of 1.0 s apart, and experience no appreciable air resistance. As time progresses, the DIFFERENCE in their speeds 19) A) remains constant. B) increases at first, but then stays constant. C) decreases. D) increases. E) decreases at first, but then stays constant. 20) Which one of the following graphs could possibly represent the vertical position as a function of time for an object in free fall? 20) A) 12 B) C) 13 D) E) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) A cat runs along a straight line (the x-axis) from point A to point B to point C, as shown in the figure. The distance between points A and C is 5.00 m, the distance between points B and C is 10.0 m, and the positive direction of the x-axis points to the right. The time to run from A to B is 20.0 s, and the time from B to C is 8.00 s. As the cat runs along the x-axis between points A and C (a) what is the magnitude of its average velocity? (b) what is its average speed? 21) 14 22) The figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s (a) what is the length of the path the object followed? (b) what is the displacement of the object? 22) 23) As part of an exercise program, a woman walks south at a speed of 2.00 m/s for 60.0 minutes. She then turns around and walks north a distance 3000 m in 25.0 minutes (a) What is the woman's average velocity during her entire motion? A) 0.824 m/s south B) 1.93 m/s south C) 2.00 m/s south D) 1.79 m/s south E) 800 m/s south (b) What is the woman's average speed during her entire motion? A) 0.824 m/s B) 1.93 m/s C) 2.00 m/s D) 1.79 m/s E) 800 m/s 23) 15 24) The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s (a) what is the average speed of the object? (b) what is the average velocity of the object? 24) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 25) If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total? 25) A) 1.0 h B) 1.3 h C) 1.4 h D) You can't stop at all. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 26) Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run? 26) 16 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h? 27) A) before marker 1 B) between marker 1 and marker 2 C) at marker 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 28) The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle? 28) 17 29) The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. for the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player. 29) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 30) The position of an object as a function of time is given by x = bt2 - ct, where b = 2.0 m/s2 and c = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2? 30) A) 2.3 m/s B) 1.7 m/s C) 2.7 m/s D) 2.1 m/s 31) The position of an object is given by x = at3 - bt2 + ct, where a = 4.1 m/s3, b = 2.2 m/s2, c = 1.7 m/s, and x and t are in SI units. What is the instantaneous acceleration of the object when t = 0.7 s? 31) A) 4.6 m/s2 B) -13 m/s2 C) 2.9 m/s2 D) 13 m/s2 32) The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s2) t2. Determine the instantaneous acceleration of the object at time t = 3.00 s. 32) A) 1.00 m/s2 B) 2.00 m/s2 C) 0.00 m/s2 D) -3.00 m/s2 E) -2.00 m/s2 18 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 33) The position of an object as a function of time is given by x(t) = at3 - bt2 + ct - d, where a = 3.6 m/s3, b = 4.0 m/s2, c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t = 2.4 s. (b) Find the average acceleration over the first 2.4 seconds. 33) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 34) The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s3)t2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s. 34) A) 1.33 m B) (3.00 m/s)t + (1.33 m/s3)t3 C) 1.00 m + (3.00 m/s)t + (1.33 m/s3)t3 D) (4.00 m/s)t E) (4.00 m/s)t + 1.00 m 35) The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? 35) A) 18.0 m/s B) 0.00 m/s C) 54.0 m/s D) 108 m/s E) 15.0 m/s 36) The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3)t, where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s? 36) A) 36.0 m B) 30.0 m C) 27.0 m D) 33.0 m 37) A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s2. How far does the car travel while accelerating? 37) A) 226 m B) 80.0 m C) 133 m D) 399 m 38) A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line? 38) A) 135 mi/h B) 269 mi/h C) 188 mi/h D) 296 mi/h 19 39) A airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of 2.40 × 102 m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane? 39) A) 2.45 m/s2 B) 5.78 m/s2 C) 7.33 m/s2 D) 4.44 m/s2 E) 1.34 m/s2 40) A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance? 40) A) 15.0 s B) 13.3 s C) 10.2 s D) 6.67 s E) 9.80 s 41) An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object? 41) A) 8.00 m/s2 B) -12.0 m/s2 C) 24.0 m/s2 D) 4.00 m/s2 E) -4.00 m/s2 42) A car starts from rest and accelerates with a constant acceleration of 1.00 m/s2 for 3.00 s. The car continues for 5.00 s at constant velocity. How far has the car traveled from its starting point? 42) A) 4.50 m B) 9.00 m C) 15.0 m D) 24.0 m E) 19.5 m 43) A ball rolls across a floor with an acceleration of 0.100 m/s2 in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball? 43) A) 5.85 m/s B) 3.85 m/s C) 4.60 m/s D) 5.21 m/s E) 4.15 m/s 20 44) A car is 200 m from a stop sign and traveling toward the sign at 40.0 m/s. At this time, the driver suddenly realizes that she must stop the car. If it takes 0.200 s for the driver to apply the brakes, what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign? 44) A) 3.89 m/s2 B) 4.17 m/s2 C) 2.89 m/s2 D) 2.08 m/s2 E) 3.42 m/s2 45) A speeding car is traveling at a constant 30.0 m/s when it passes a stationary police car. If the police car delays for 1.00 s before starting, what must be the magnitude of the constant acceleration of the police car to catch the speeding car after the police car travels a distance of 300 m? 45) A) 3.00 m/s2 B) 3.70 m/s2 C) 7.41 m/s2 D) 6.00 m/s2 E) 1.45 m/s2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 46) A soccer ball is released from rest at the top of a grassy incline. After 8.6 seconds, the ball travels 87 meters and 1.0 s after this, the ball reaches the bottom of the incline. (a) What was the magnitude of the ball's acceleration, assume it to be constant? (b) How long was the incline? 46) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 47) A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released if air resistance is negligible? 47) A) 810 m B) 1000 m C) 1500 m D) 1200 m 48) A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 36.2 m/s if air resistance is negligible. The time when the ball strikes the ground is closest to 48) A) 10 s. B) 9.4 s. C) 8.7 s. D) 9.7 s. E) 9.0 s. 21 49) At the same moment from the top of a building 3.0 × 102 m tall, one rock is dropped and one is thrown downward with an initial velocity of 10 m/s. Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground? 49) A) 0.86 s B) 0.95 s C) 0.67 s D) They land at exactly the same time. 50) Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. If object B takes TWICE as long as object A to reach the ground, what is the ratio of the heights from which A and B fell? 50) A) hA/hB = 1/4 B) hA/hB = 1/2 C) hA/hB = 1/ 2 D) hA/hB = 1/8 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 51) A foul ball is hit straight up into the air with a speed of 30.0 m/s. (a) Calculate the time required for the ball to rise to its maximum height. (b) Calculate the maximum height reached by the ball. (c) Determine the time at which the ball pass a point 25.0 m above the point of contact between the bat and ball. (d) Explain why there are two answers to part (c). 51) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 52) A rock is dropped from the top of a vertical cliff and takes 3.00 s to reach the ground below the cliff. A second rock is thrown vertically from the cliff, and it takes this rock 2.00 s to reach the ground below the cliff from the time it is released. With what velocity was the second rock thrown, assuming no air resistance? 52) A) 4.76 m/s upward B) 5.51 m/s downward C) 4.76 m/s downward D) 12.3 m/s upward E) 12.3 m/s downward 53) To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.) 53) A) 16 m B) 18 m C) 13 m D) 10 m E) 26 m 54) A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s2. After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach? 54) A) 160 m B) 408 m C) 320 m D) 487 m E) 327 m 22 55) A toy rocket is launched vertically from ground level (y = 0.00 m), at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 72 m and acquired a velocity of 30 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to 55) A) 39 m/s. B) 54 m/s. C) 44 m/s. D) 59 m/s. E) 48 m/s. 56) A ball is projected upward at time t = 0.00 s, from a point on a roof 70 m above the ground and experiences negligible air resistance. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 28.5 m/s. Consider all quantities as positive in the upward direction. The velocity of the ball when it is 39 m above the ground is closest to 56) A) -38 m/s. B) -15 m/s. C) -30 m/s. D) -23 m/s. E) -45 m/s. 57) On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is 57) A) g/ 2. B) 2g. C) g 2. D) g/2. E) g/4. 58) Two identical stones are dropped from rest and feel no air resistance as they fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time 58) A) 2t. B) t 2. C) t/2. D) t/ 2. E) 4t. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 59) A rock is thrown directly upward from the edge of the roof of a building that is 66.2 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any effects of air resistance. With what speed was the rock thrown? 59) 60) A rocket takes off vertically from the launchpad with no initial velocity but a constant upward acceleration of 2.25 m/s2. At 15.4 s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity. (a) What is the maximum height the rocket will reach above the launchpad? (b) How fast is the rocket moving at the instant before it crashes onto the launchpad? (c) How long after engine failure does it take for the rocket to crash onto the launchpad? 60) 23 Answer Key Testname: UNTITLED2 1) B 2) A 3) B 4) D 5) B 6) B 7) C 8) B 9) (a) J (b) I 10) B 11) A 12) B 13) E 14) D 15) A 16) A 17) C 18) B 19) A 20) D 21) (a) 0.179 m/s (b) 0.893 m/s 22) (a) 5.0 m (b) 1.0 m 23) (a) A (b) C 24) (a) 0.56 m/s (b) 0.11 m/s 25) B 26) 100 m 27) A 28) (a) 1.0 m/s (b) 0.00 m/s 29) (a) 18 m (b) 20 m 30) D 31) D 32) D 33) (a) 44 m/s2 (b) 18 m/s2 34) C 35) C 36) C 37) C 38) B 39) C 40) D 41) A 42) E 43) E 44) B 45) C 46) (a) 2.4 m/s2 (b) 110 m 47) B 24 Answer Key Testname: UNTITLED2 48) B 49) B 50) A 51) (a) 3.06 s (b) 45.9 m (c) 0.995 s and 5.13 (d) One value is for the ball traveling upward; one value is for the ball traveling downward. 52) E 53) D 54) D 55) E 56) A 57) D 58) B 59) 3.05 m/s 60) (a) 328 m (b) 80.2 m/s (c) 11.7 s 25