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- A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69arrow_forwardLet us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?arrow_forwardFor the two vectors find A − B and |A – B| component of B along A angle between A and B A × B (A − B) × (A + B)arrow_forward
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- E Vectors → and are shown in the figure. Vector is given by →→→→. The magnitude of A B C C B A vectoris 16.0 units, and the magnitude of vectoris 7.00 units. What is the angle of vector, A B measured counterclockwise from the +x-axis? 41.0 F4 S4 31.0 B 73.1° 287° F5 R % 5 V F6 T G Bi F7 B C H F8 & 7 00 D F9 * 00 J N M F10 K F11 FO: L F12 P PrtScr [ Insert ? 81°F Sunny ^ Delete Backspace ] PgUparrow_forwardThe vector product of vectors A → and B → has magnitude 12.0 m2m2 and is in the +z+-direction. Vector A → has magnitude 4.0 mm and is in the −x− -direction. Vector B → has no x-component. What is the directional angle θ of vector B → in the xy-plane measured counterclockwise from the +x+ -direction?arrow_forwardVectors A, B and C are defined as follows: A = 3.1i + 2.7j – 4.3k; B = 2.5i – 3.7j + 7.7k; C = 3.9i + 6.6k. Determine A·(B×C)arrow_forward
- For the vectors in the figure, with a 12, b-9.0, and c-15 what are (a) the magnitude and (b) the direction of a x b. (c) the magnitude and (d) the direction of ax, and (e) the magnitude and (f) the direction bx ? A (a) (b) (c) (d) (e) (f) 108 37 i 108arrow_forwardConsider the two vectors A-5i-j and B = - i- 4j. (a) Calculate A+B i+ (b) Calculate A -R i (c) Calculate A+ E (d) Calculate A - E (e) Calculate the directions of A +B and A-B. * (counterclockwise from the +x axis) A - B * (counterclockwise from the +x axis)arrow_forwardA student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y(x) = ax² + bx where a = −8.0 × 10−³ m−¹, b = 1.0 (unitless), x is the horizontal position along the pumpkin trajectory and y is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height. What is the derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position? ▸ View Available Hint(s) dy dx = 2ax + b dy dx dy dx dy dx - 0 = 2ax axarrow_forward
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