82 CHAPTER 3 VECTORS IN PHYSICS how do you predict your answers to parts (a) and (b) will change? 12. . . A baseball "diamond" (FIGURE 3-38) is a square with sides 90 ft in (d) Verify your prediction in part (c) by calculating the magnitude length. If the positive x axis points from home plate to first base, and direction for this new case. and the positive y axis points from home plate to third base, find 16. .. You drive a car 680 ft to the east, then 340 ft to the north. (a) What the displacement vector of a base runner who has just hit (a) a is the magnitude of your displacement? (b) Using a sketch, esti- double, (b) a triple, or (c) a home run. mate the direction of your displacement. (c) Verify your estimate in part (b) with a numerical calculation of the direction. 17. .. Vector A has a magnitude of 50 units and points in the positive x direction. A second vector, B , has a magnitude of 120 units and points at an angle of 70 below the x axis. Which vector has (a) the greater x component, and (b) the greater y component? 90 ft 18. . . A treasure map directs you to start at a palm tree and walk due north for 15.0 m. You are then to turn 90 and walk 22.0 m; then turn 90 again and walk 5.00 m. Give the distance from the palm tree, and the direction relative to north, for each of the four pos- sible locations of the treasure. FIGURE 3-38 Problem 12 . . A whale comes to the surface to breathe and then dives at an angle of 20.0 below the horizontal (FIGURE 3-41). If the whale . . A lighthouse that rises 49 ft above the surface of the water sits continues in a straight line for 215 m, (a) how deep is it, and on a rocky cliff that extends 19 ft from its base, as shown in FIGURE (b) how far has it traveled horizontally? 3-39. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30.0 above the horizontal. If the sailor's eye level is 14 ft above the water, how far is the ship from the rocks? 20.00 49 ft O 30.0% FIGURE 3-41 Problem 19 14 ft SECTION 3-3 ADDING AND SUBTRACTING VECTORS - 19 ft- 20. . CE Consider the vectors A and B shown in FIGURE Which of the other four vectors in the figure (C, D, E F) best represents the direction of (a) A + B, (b) A - B FIGURE 3-39 Problem 13 (C) B - A? 55 . . Predict/Calculate The pilot of an airplane wishes to fly due north, but there is a 65-km/h wind blowing toward the east. (a) In what direction relative to north should the pilot head her plane if its speed relative to the air is 340 km/h? (b) Draw a vector diagram that illustrates your result in part (a). (c) If the pilot decreases the air speed of the plane, but still wants to head due north, should the angle found in part (a) be increased or decreased? 56. .. A passenger walks from one side of a ferry to the other as it B approaches a dock. If the passenger's velocity is 1.50 m/s due north relative to the ferry, and 4.50m/s at an angle of 30.0 west of north relative to the water, what are the direction and magnitude of the ferry's velocity relative to the water? URE 3-42 Problems 20 and 21 $7. .. You are riding on a Jet Ski at an angle of 35 upstream on a river flowing with a speed of 2.8 m/s. I fer to Figure 3-42 for the following questions de of A' + D' greater than, less than, or equalDIS Of A ? 12. Use a sketch to show that two vectors of unequal magnitude cannot add to zero, but that three vectors of unequal magnitude can. 13. Rain is falling vertically downward and you are running for shel- ter. To keep driest, should you hold your umbrella vertically, tilted forward, or tilted backward? Explain. 14. When sailing, the wind feels stronger when you sail upwind ("beat- ing") than when you are sailing downwind ("running"). Explain. he back of the book. BIO identifies problems of biological or medical interest; onses: (a) your prediction of a physical outcome, and (b) the best explanation a physical outcome, based on fundamental physics concepts, and follow that .., ..) indicate the level of difficulty. . The press box at a baseball park is 44.5 ft above the ground. A reporter in the press box looks at an angle of 13.4 below the hori- zontal to see second base. What is the horizontal distance from the press box to second base? 6. . You are driving up a long, inclined road. After 1.2 miles you notice that signs along the roadside indicate that your elevation has increased by 530 ft. (a) What is the angle of the road above the horizontal? (b) How far do you have to drive to gain an additional 150 ft of elevation? 7. . A One-Percent Grade A road that rises 1 ft for every 100 ft traveled horizontally is said to have a 1% grade. Portions of the Lewiston grade, near Lewiston, Idaho, have a 6% grade. At what angle is this road inclined above the horizontal? . You walk in a straight line for 95 m at an angle of 162 above the pos- itive x axis. What are the x and y components of your displace