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You are on the Pirates of the Caribbean attraction in the Magic kingdom at Disney World. Your boat rules through a pirate battle, in which cannons on a ship and in a fort are firing at each other. While you are aware that the splashes in the water do not represent actual cannonballs, you begin to wonder about such battles in the days of the pirates. Suppose the fort and the ship are separated by 75.0 m. You sec that the cannons in the fort are aimed so that their cannonballs would be fired horizontally from a height of 7.00 m above the water. (a) You wonder at what speed they must be fired in order to hit the ship before falling in the water. (b) Then, you think about the sludge that must build up inside the barrel of a cannon. This sludge should slow down the cannonballs. A question occurs in your mind: if the cannonballs can be fired at only 50.0% of the speed found earlier, is it possible to fire them upward at some angle to the horizontal so that they would reach the ship?
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Chapter 4 Solutions
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- Figure OQ1.13 shows two vectors D1 and D2. Which of the possibilities (a) through (d) is the vector D22D1, or (e) is it none of them? Figure OQ1.13arrow_forwardA 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 P3.46. 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 P3.46arrow_forwardWhat is the x component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answersarrow_forward
- The same vectors that are shown in Figure P3.6 are shown in Figure P3.42. The magnitudes are F1 = 1.90f, F2 = f, and F3 = 1.4f, where f is a constant. a. Use the coordinate system shown in Figure P3.42 to find R=F1+F2+F3 in component form in terms of f. b. If Rx = 0.33, what is Ry? c. Check your result by comparing your answer to that of Problem 6. FIGURE P3.42arrow_forwardCheck Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?arrow_forward1. Find the following for path A in Figure 3.52: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish. N w -E S Start B- D Figure 3.52 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side. 2. Find the following for path B in Figure 3.52: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.arrow_forward
- a.) Vector A has a magnitude of 6.0 m and points 30° north of east. Vector B⃗ has a magnitude of 4.0 m and points 30° east of north. What is the magnitude of the sum, A +B? b.) What is the direction of the sum A +B, measured counterclockwise from east?arrow_forwardA rectangular parallelepiped has dimensions a, b, and c as shown in Figure P3.45. (a) Obtain a vector expression for the face diagonal vector R,. (b) What is the magnitude of this vector? (c) Notice that R, ck, and R, make a right triangle. Obtain a vector expression for the body diagonal vector R2. b Ro R1 Figure P3.45arrow_forwardConsider two vectors C & D in XY-plane, shown in the figure beside. If C-D-12 m and a-30, the vector C (in m) is: -6 i+10.4j O 10 i+8.3j -10.4i +6j O5.5i+6.4j O 2.5i+ 8.6jarrow_forward
- Three archers each fire four arrows at a target. Joe’s four arrows hit points that are spread around in a region that goes 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm from the center, and Flo’s four arrows hit within 1 cm of the center. The contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. Which description applies to which archer? Explain.arrow_forward18. Use the component method to add the vectors A and B shown in Figure P3.11. Both vectors have magnitudes of 3.00 m and vector A makes an angle of 0 = 30.0° with the x axis. Express the resultant Á + B in unit-vector notation, %3D 95 19. A vector haarrow_forwardThree displacement vectors of a cro- quet ball are shown in Figure P3.22, where A| = 40.0 units, and |C| = 30.0 units. Find (a) the resultant in unit-vector nota- tion and (b) the magnitude and direc- tion of the resultant displacement. 20.0 units, B|arrow_forward
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