Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 1

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1 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 1 This print-out should have 73 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Rectangular vs Polar 001 (part 1 of 2) 10.0 points The rectangular and polar coordinates of a point are (x, y) and (r, θ), where x = 9 and θ = 61. Determine the value of r. Correct answer: (part 2 of 2) 10.0 points Determine the value of y. Correct answer: Perpendicular Displacements points Two airplanes leave an airport at the same time. The velocity of the first airplane is 700 m/h at a heading of The velocity of the second is 620 m/h at a heading of 107. How far apart are they after 1.9 h? Correct answer: m. Adding Vectors points A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is correct Trig Solutions 005 (part 1 of 2) 10.0 points Consider two vectors A and B and their resultant A+ B. The magnitudes of the vectors A and B are, respectively, 13.2 and 8.2 and they act at 45 to each other. B A + B A Find the magnitude of the resultant vector A + B. Correct answer: (part 2 of 2) 10.0 points Find the angle between the direction of the resultant vector A + B and the direction of the vector A. Correct answer: Holt SF 03Rev 50 graph points A hunter wishes to cross a river that is 1.3 km wide and that flows with a speed of 8 km/h. The hunter uses a small powerboat that moves at a maximum speed of 14 km/h with respect to the water. What is the time necessary for crossing if the hunter wishes to move neither upstream nor downstream whilst crossing the river? Draw the vectors to scale on a graph to determine the answer. Correct answer: min. Sum of Three Vectors 01 graph 008 (part 1 of 2) 10.0 points Consider three force vectors F 1, F 2, and F 3 with magnitude 72 N and direction 155 ; magnitude 98 N and direction 271 ; and magnitude 54 N and direction 84, respectively. All direction angles are measured from the positive x axis: counter-clockwise for θ > 0 and clockwise for θ < 0. What is the magnitude of the resultant vector F, where F = F 1 + F 2 + F 3? Draw the vectors to scale on a graph to determine the answer. Your answer must be within ± 5.0%

2 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 2 Correct answer: 60 N. 009 (part 2 of 2) 10.0 points What is the direction of this resultant vector F? Use counterclockwise as the positive angular direction, between the limits of 180 and +180 from the positive x axis. Your answer must be within ± 5.0% Correct answer: 166. Directions to Your House points When giving directions to your house, you tell someone to drive two miles east, then three miles north, then one mile west. What are the components of a vector that points from his house to yours? 1. The west component of the vector is 1 mile; the north component is 3 miles. 2. The west component of the vector is three miles; the north component is 3 miles. 3. The east component of the vector is 1 mile; the north component is 3 miles. correct 4. The west component of the vector is 1 mile; the south component is 3 miles. 5. The east component of the vector is three miles; the south component is 3 miles. 6. None of these 7. The east component of the vector is 1 mile; the south component is 3 miles. Holt SF 03B (part 1 of 2) 10.0 points A skier squats low and races down an 18 ski slope. During an 8 s interval, the skier accelerates at 1.6 m/s 2. What is the horizontal component of the skier s acceleration (perpendicular to the direction of free fall)? Correct answer: m/s (part 2 of 2) 10.0 points What is the vertical component of the skier s acceleration? Correct answer: m/s 2. Magnitude of a Vector 013 (part 1 of 2) 10.0 points Vector B has x, y, and z components of 9.6, 6, and 8.5 units, respectively. Calculate the magnitude of B. Correct answer: (part 2 of 2) 10.0 points What is the angle between B and the x-axis? Correct answer: Vector Components (part 1 of 3) 10.0 points The weight of a ball rolling down an inclined plane can be broken into two vector components: one acting parallel to the plane, and the other acting perpendicular to the plane. At what angle of inclination of the plane are these two components equal? Correct answer: (part 2 of 3) 10.0 points At what angle of inclination of the plane will the parallel component be equal to zero? Correct answer: (part 3 of 3) 10.0 points At what angle of inclination of the plane will the parallel component be equal to the weight? Correct answer: 90. Sum of Two Vectors 01 graph 018 (part 1 of 2) 10.0 points Given two vectors F 1, and F 2. Where the magnitude of these vectors are F 1 = 96 N,

3 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 3 and F 2 = 78 N. And where θ 1 = 335, and θ 2 = 74. The angles are measure from the positive x axis with the counter-clockwise angular direction as positive. Draw the vectors to scale on a graph to determine the answer. What is the magnitude of the resultant vector F, where F = F 1 + F 2? Correct answer: N. 019 (part 2 of 2) 10.0 points Note: Give the angle in degrees, use counterclockwise as the positive angular direction, between the limits of 180 and +180 from the positive x axis. What is the direction of this resultant vector F? 4. correct Correct answer: Vector Difference points Consider the vectors A and B. A Which sketch shows the vector A B to the same scale? B 8. Cartesian Coordinates 021 (part 1 of 2) 10.0 points Two points have cartesian coordinates (8.7 m, 10 m) and ( 10 m, 7.5 m). Find the distance between these points. Correct answer: m (part 2 of 2) 10.0 points What is the angle between the line connecting the two points and the x-axis (measured counter-clockwise from the x-axis and within the limits of 180 to +180 )? Correct answer: Commuter Plane Trip 023 (part 1 of 5) 10.0 points A commuter airplane starts from an airport located at the origin. First it flies to city A located 110 km away from the airport in

4 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 4 a direction 34 North of East. Next it flies 64.6 km at 31 West of North to city B. Finally it flies 168 km due West to city C. C W r c O B b a α What is the x-component of the vector b? Consider E to be the positive x axis and N to be the positive y axis. 1. b x = b tanβ 2. b x = b tanβ 3. b x = b cosβ 4. b x = b cos β γ N 5. b x = b sin β correct 6. b x = b sinβ 024 (part 2 of 5) 10.0 points What is the y-component of the vector b? 1. b y = b tanβ 2. b y = b sinβ 3. b y = b cos β 4. b y = b sin β 5. b y = b tanβ 6. b y = b cosβ correct 025 (part 3 of 5) 10.0 points What is the x-component of vector r from the starting point (position O) to the city C? Correct answer: km. 026 (part 4 of 5) 10.0 points What is the y-component of vector r? β N A E Correct answer: km. 027 (part 5 of 5) 10.0 points What is the direction of the final position vector r in degrees West of North; i.e., what is the angle γ? Use counterclockwise as the positive angular direction, measured between 180 and +180 from North; (e.g., East is 90 ). Correct answer: Particle in a Plane 028 (part 1 of 3) 10.0 points A particle starts from the origin at t = 0 with an initial velocity having an x component of 28.2 m/s and a y component of 19.9 m/s. The particle moves in the xy plane with an x component of acceleration only, given by 5.24 m/s 2. Determine the x component of velocity after 7.49 s. Correct answer: m/s. 029 (part 2 of 3) 10.0 points Find the speed of the particle after 7.49 s. Correct answer: m/s. 030 (part 3 of 3) 10.0 points Find the magnitude of the displacement vector of the particle after 7.49 s. Correct answer: m. Serway CP (part 1 of 3) 10.0 points A girl delivering newspapers covers her route by traveling 2 blocks west, 1 blocks north, then 5 blocks east. What is her resultant displacement? Correct answer: blocks. 032 (part 2 of 3) 10.0 points What is her direction? Use counterclockwise as the positive angular direction from due

5 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 5 east, between the limits of 180 and 180. Correct answer: (part 3 of 3) 10.0 points What is her total distance? 15 m Correct answer: 8 blocks. Vector Addition (part 1 of 2) 10.0 points Let a A + b B + C = 0, where A = (3.8, 65), B = ( 59, 25), and C = (28, 91). What is the value of a? Correct answer: (part 2 of 2) 10.0 points What is the value of b? Correct answer: Vector Subtraction points Vector A has a magnitude of 10 and points in the positive x-direction. Vector B has a magnitude of 23 and makes an angle of 37 with the positive x-axis. What is the magnitude of A B? Correct answer: Zero Displacement 037 (part 1 of 2) 10.0 points A particle undergoes three displacements. The first has a magnitude of 15 m and makes an angle of 42 with the positive x axis. The second has a magnitude of 8.4 m and makes an angle of 166 with the positive x axis. (see the figure below). After the third displacement the particle returns to its initial position. 8.4 m Find the magnitude of the third displacement. Correct answer: m. 038 (part 2 of 2) 10.0 points Find the angle of the third displacement (measured from the positive x axis, with counterclockwise positive within the limits of 180 to +180 ). Correct answer: Math review for vectors points Consider the vector M = (+c, +d) = +c î + d ĵ. d a c b d E F H a c b A D d b c a d b c a Which vector is a valid representation of M? y B G C x 1. F and G, but no others. correct 2. F, H, B, and G, but no others. 3. A and D, but no others.

6 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 6 4. B and H, but no others. 5. F only. 6. E, A, D, and C, but no others. 7. E only. 8. C only. 9. E and C, but no others. 10. G only. Vector Addition points Let A = i, B = i + j and C = j. Find the magnitude of D = A+B+C and the polar angle θ D. 1. D = 2 2, θ D = 45 correct 2. D = 2, θ D = D = 2, θ D > D = 2 2, θ D > 45 Ant Walk points An ant starts at one edge of a long strip of paper that is 34.9 cm wide. She travels at 2.6 cm/s at an angle of 15 with the long edge. How long will it take her to get across? Correct answer: s. Holt SF 03Rev (part 1 of 4) 10.0 points A shopper pushing a cart through a store moves 30.0 m south down one aisle, then makes a 90 turn and moves 17.0 m. He then makes another 90 turn and moves 29.0 m. What is the magnitude of the smallest possible displacement the shopper could have? You are not given the direction moved after any of the 90 turns, so there could be more than one answer. Correct answer: m. 043 (part 2 of 4) 10.0 points At how many degrees from due south is this displacement? Correct answer: (part 3 of 4) 10.0 points What is the magnitude of the largest possible displacement the shopper could have? Correct answer: m. 045 (part 4 of 4) 10.0 points At how many degrees from due south is this displacement? Correct answer: Scalar Product (part 1 of 2) 10.0 points The vectors A and B are given by A = 2.67î+5.96ĵ and B = 3.03î+5.33ĵ. Find the scalar product A B. Correct answer: (part 2 of 2) 10.0 points Find the angle between A and B. Correct answer: Math review for vectors (part 1 of 3) 10.0 points Consider the two vectors M = (a, b) = a î+b ĵ and N = (c, d) = c î + d ĵ, where a = 4, b = 4, c = 2, and d = 2. a and c represent the x-displacement and b and d represent the y- displacement in a Cartesian xy coordinate system. What is the magnitude of the vector product M M? Correct answer: 0.

7 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) (part 2 of 3) 10.0 points What is the magnitude of the vector product M N? Correct answer: (part 3 of 3) 10.0 points What is the direction of the vector product M N? 1. In the xy plane, but not along x or y 2. Along the y-axis 3. Along the z-axis correct 4. None of these; its direction cannot be determined. 5. Along the x-axis 6. In the xz plane, but not along x or z 7. In the yz plane, but not along y or z Particle Motion (part 1 of 2) 10.0 points A particle has r(0) = (4 m) ĵ and v(0) = (2 m/s) î. If its acceleration is constant and given by a = (2 m/s 2 ) (î+ĵ), at what time t does the particle first cross the x axis? Correct answer: 2 s. 052 (part 2 of 2) 10.0 points At what time t is the particle moving parallel to the y axis; that is, in the ĵ direction? Correct answer: 1 s. Frustrated With It All 053 (part 1 of 2) 10.0 points A disgruntled physics student, frustrated with finals, releases his tensions by bombarding the adjacent building, 15.3 m away, with water balloons. He fires one at 37 from the horizontal with an initial speed of 29.1 m/s. The acceleration of gravity is 9.8 m/s 2. For how long is the balloon in the air? s correct s s s s s s s 054 (part 2 of 2) 10.0 points How far above the initial launch height does the balloon hit the opposing building? m m m m m correct m m m Monkey and Coconut (part 1 of 3) 10.0 points A boy is standing on a cliff. The boy s hands are a height b above the ground level at the base of the cliff. A monkey is in a tree. The monkey is at a height h above the boy s hands. At t = 0 the boy throws a coconut upward at a speed v 0, and at the same time the monkey releases his grip, falling downward to catch the coconut.

8 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 8 Assume the initial speed of the monkey is 0 m/s, and the cliff is high enough so that the monkey is able to catch the coconut before hitting the ground. The acceleration of gravity is 10 m/s 2. h C v 0 monkey height 9. t = v 0 2 g + h 2 v t = h v 0 correct 056 (part 2 of 3) 10.0 points Suppose it takes 2 s for the monkey to catch the coconut and the initial upward speed of the coconut is 5 m/s. Let the y coordinate of the ground, the boy, and the monkey be, respectively, y A = b, y B = 0, and y C = h. What is the y coordinate of the location where the monkey catches the coconut? B hand height 1. y = 20 m 2. y = +10 m b A ground level Figure: Consider only vertical motion. How long t does it take for the monkey to reach the coconut? 1. t = h 2 v 0 2 h 2. t = g 3. t = v 0 g 2 h 4. t = g + v 0 g 5. t = v 0 2 g 2 h 6. t = g + h 2 v 0 7. t = 2 v 0 g 8. t = 2 h v 0 3. y = +8 m 4. y = +15 m 5. y = 10 m correct 6. y = 5 m 7. y = +5 m 8. y = 0 m 9. y = +9 m 10. y = +2 m 057 (part 3 of 3) 10.0 points Caution: Let upward motion be associated with positive velocity. Using the same numerical values as part 2, what is the velocity v of the coconut just before the monkey catches the coconut? 1. v = +15 m/s 2. v = 5 m/s 3. v = +10 m/s 4. v = +25 m/s

9 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) 9 5. v = +0 m/s 6. v = 10 m/s 7. v = +20 m/s 8. v = 15 m/s correct 9. v = 20 m/s 10. v = +5 m/s Cannon (part 1 of 5) 10.0 points A projectile of mass kg is shot from a cannon, at height 7 m, as shown in the figure, with an initial velocity v i having a horizontal component of 6.8 m/s. The projectile rises to a maximum height of y above the end of the cannon s barrel and strikes the ground a horizontal distance x past the end of the cannon s barrel. x v i 58 7 m y Find the vertical component of the initial velocity at the end of the cannon s barrel, where the projectile begins its trajectory. The acceleration of gravity is 9.8 m/s 2. Correct answer: m/s. 059 (part 2 of 5) 10.0 points Determine the maximum height the projectile achieves after leaving the end of the cannon s barrel. Correct answer: m. 060 (part 3 of 5) 10.0 points Find the magnitude of the velocity vector when the projectile hits the ground. Correct answer: m/s. 061 (part 4 of 5) 10.0 points Find the magnitude of the angle (with respect to horizontal) the projectile makes when impacting the ground. Correct answer: (part 5 of 5) 10.0 points Find the range of the projectile from the time it leaves the barrel until it hits the ground. Correct answer: m. Electron in a Television points In a TV set, an electron beam moves with horizontal velocity of m/s across the cathode ray tube and strikes the screen, 44 cm away. The acceleration of gravity is 9.8 m/s 2. How far does the electron beam fall while traversing this distance? Correct answer: m. Holt SF 03Rev (part 1 of 3) 10.0 points A ball player hits a home run, and the baseball just clears a wall 8.00 m high located m from home plate. The ball is hit at an angle of 38.1 to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.0 m above the ground. The acceleration of gravity is 9.81 m/s 2. a) What is the initial speed of the ball? Correct answer: m/s. 065 (part 2 of 3) 10.0 points b) How much time does it take for the ball to reach the wall? Correct answer: s.

10 Version PREVIEW Vectors & 2D Chap. 3 sizemore (13756) (part 3 of 3) 10.0 points c) Find the speed of the ball when it reaches the wall. Correct answer: m/s. Projectile Graph (part 1 of 2) 10.0 points Before coming to Earth, your teacher was on planet Krypton where there was almost no atmosphere. Your teacher observed and plotted the position of a projectile at constant time intervals of 0.18 s, as shown in the figure. Vertical Distance (m) Projectile Position on Planet Krypton Horizontal Distance (m) Figure: Drawn to scale. Calculate the horizontal velocity of the projectile. Correct answer: m/s. 068 (part 2 of 2) 10.0 points Calculate the vertical acceleration due to the gravity of planet Krypton on the projectile. Correct answer: m/s 2. Serway CP points One of the fastest recorded pitches in majorleague baseball, thrown by Nolan Ryan in 1974, was clocked at 96.4 mi/h. The acceleration of gravity is 32 ft/s 2. If a pitch were thrown horizontally with a velocity of 96.4 mi/h, how far would the ball fall vertically by the time it reached home plate, 60 ft away? Correct answer: ft. Serway CP (part 1 of 2) 10.0 points Tom the cat is chasing Jerry the mouse across a table surface 2.2 m off the floor. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 2.7 m/s. The acceleration of gravity is 9.8 m/s 2. Where will Tom strike the floor? Correct answer: m. 071 (part 2 of 2) 10.0 points What speed will Tom have just before he hits? Correct answer: 7.1 m/s. Tipler PSE (part 1 of 2) 10.0 points Wiley Coyote (Carnivouous hungribilous) is chasing the roadrunner (Speediburd cantcatchmi) yet again. While running down the road, they come to a deep gorge, 17 m straight across and 72 m deep. The roadrunner launches itself across the gorge at a launch angle of 13 above the horizontal, and lands with 2.1 m to spare. The acceleration of gravity is 9.81 m/s 2. What was the roadrunner s launch speed? Ignore air resistance. Correct answer: m/s. 073 (part 2 of 2) 10.0 points Wiley Coyote launches himself across the gorge with the same initial speed, but at a lower launch angle. To his horror, he is short of the other lip by 1.2 m and falls into the gorge. What was Wiley Coyote s launch angle? Correct answer:

Components of a Vector

Components of a Vector Vectors (Ch. 1) A vector is a quantity that has a magnitude and a direction. Examples: velocity, displacement, force, acceleration, momentum Examples of scalars: speed, temperature, mass, length, time.