th Google Docs For Thought and Discussion d are pos 1. Under what conditions is the magnitude of the vector sum tion of the A + B equal to the sum of the magnitudes of the two vectors? 22. A car, in 2. Can two vectors of equal magnitude sum to zero? How about two up headi vectors of unequal magnitude? Repeat for three vectors constant 3. Can an object have a southward acceleration while moving north- vector? ward? A westward acceleration while moving northward? 23. What are 4. You're a passenger in a car rounding a curve. The driver claims of the tip the car isn't accelerating because the speedometer reading is un- val from changing. Explain why the driver is wrong. pointing to 5. In what sense is Equation 3.8 really two (or three) equations? 24. An object 6. Is a projectile's speed constant throughout its parabolic trajectory? ation that 7. Is there any point on a projectile's trajectory where velocity and of motion, acceleration are perpendicular? the angle b 8. How is it possible for an object to be moving in one direction but tion of the accelerating in another? 25. An object 9. You're in a bus moving with constant velocity on a level road dergoes an when you throw a ball straight up. When the ball returns, does after 4.4 s. it land abead of you, behind you, or back at your hand? Explain. 10. Which of the following are legitimate mathematical equa- Section 3.3 tions? Explain. (a) v - Si m/s: (b) i = 5 m/s; (c) a - hildr, 26. You're pilo (d) a - hildr. (e) i - Sim/s. a wind blow speed (i.c.. Exercises and Problems rection shou 27. You wish to Exercises at a steady 0.57 m/s. (a) Section 3.1 Vectors it take you to 11. You walk 157 km north, then 0.846 km cast. Find (a) the magni- 28. A plane with tude of your displacement vector and (b) its direction, expressed the jet stream as an angle relative to the northward direction. flight directi 12. An ion in a mass spectrometer follows a semicircular path of ra- 29. A flock of ge dius 15.2 cm. What are (a) the distance it travels and (b) the mag- is blowing fr nitude of its displacement? relative to the 13. A migrating whale follows the coast of Mexico and California. It first travels 360 km northwest, then turns due north and travels an- Section 3.4 C other 410 km. Determine graphically the magnitude and direction 30. The position of its displacement F = (3.21 + 14. Vector A has magnitude 3.0 m and points to the right; vector B Find the obje has magnitude 4.0 m and points vertically upward. Find the mag- 31. You're sailbo nitude and direction of vector C such that A + B + C = 0. 6.3 s and acce 15. Use unit vectors to express a displacement of 120 km at 29 inal direction counterclockwise from the a-axis. ment during 16. Find the magnitude of the vector angle to the 1-axis Section Page 1 17. (a) What's the magnitude of i + You with the J-axis?Three Dimensions 21. An object's velocity is v = cri + dj, where t is time and c and . . . d are positive constants with appropriate units. What's the direc. sion tion of the object's acceleration? magnitude of the vector sum 22. A car, initially going eastward, rounds a 90 curve and ends Section 3.6 Uniform Circular magnitudes of the two vectors? up heading southward. If the speedometer reading remains 38. China's high-speed rail network le sum to zero? How about two constant, what's the direction of the car's average acceleration of 7.0 km for 350-km/h trains. vector? acceleration in this case? peat for three vectors. eleration while moving north- 23. What are (a) the average velocity and (b) the average acceleration 39. The minute hand of a clock is 7 of the acceleration of its tip. ile moving northward? of the tip of the 2.4-cm-long hour hand of a clock in the inter. 40. How fast would a car have to ng a curve. The driver claims val from noon to 6 PM? Use unit vector notation, with the x-axis pointing toward 3 and the y-axis toward noon. acceleration to be numerically e e speedometer reading is un- 41. Determine the acceleration of wrong. 24. An object is moving with speed v when it's subject to an acceler- nearly circular orbit of 384.4 M two (or three) equations? hout its parabolic trajectory? ation that leaves it moving at an angle 0 to its original direction 42. Global Positioning System (C of motion, with twice its original speed. Find an expression for tudes of approximately 20,000 jectory where velocity and the angle between the acceleration vector and the original direc- eration has 5.8% of its surface tion of the object's motion. the orbital period of the GPS moving in one direction but 25. An object is moving in the x-direction at 1.3 m/s when it un- 43. Pilots of high-performance air velocity on a level road dergoes an acceleration a = 0.52) m/s. Find its velocity vector they undergo accelerations ex flying at 2470 km/h (about tv hen the ball returns, does after 4.4 s. minimum radius for a turn that k at your hand? Explain. Section 3.3 Relative Motion te mathematical equa- Example Variations = 5 m/s; (c) a = dvldt; 26. You're piloting a small plane on a route directly north, but there's The following problems are based a wind blowing from the west at 59.8 km/h. If your plane's air- set of four problems is designed speed (i.e., its speed relative to the air) is 465 km/h, in what di- enhance your understanding of rection should you head? in solving problems that differ fro 27. You wish to row straight across a 63-m-wide river. You can row problem in each set is essentially at a steady 1.3 m/s relative to the water, and the river flows at ent numbers. The second proble 0.57 m/s. (a) What direction should you head? (b) How long will example but asks a different que it take you to cross the river? repeat this pattern but with entire t. Find (a) the magni- 28. A plane with airspeed 370 km/h flies a course perpendicular to 44. Exam You're wind direction, expressed the jet stream, its nose pointed into the jet stream at 32 from its accelerating your sailboard n. flight direction. Find the speed of the jet stream. direction. If the gust lasts nicircular path of ra- 29. A flock of geese is attempting to migrate due south, but the wind board's displacement durin els and (b) the mag- is blowing from the west at 5.1 m/s. If the birds can fly at 7.5 mls 45. Examp You're wind relative to the air, what direction should they head? celerating your sailboard at o and California. It lasts 5.42 s, and the board's orth and travels an- Section 3.4 Constant Acceleration Find the magnitude of the itude and direction 30. The position of an object as a function of time is given by 46. Example 3 A hockey 7 = (3.21 + 1.812)1 + (1.7t - 2.412)jm, with t in seconds. when a player whacks it e right; vector B celeration of 448 m/s2 d. Find the mag- Find the object's acceleration vector. B + C = 0. 31. You're sailboarding at 6.5 m/s when a wind gust hits, lasting acceleration lasts 41.3 120 km at 290 6.3 s and accelerating your board at 0.48 m/s at 35 to your orig displacement during this inal direction. Find the magnitude and direction of your displace- 47. Example 3.3 A hockey when a player whacks it d determine its ment during the gust. celeration at 64.3 to its 50.3 ms, and the puck's e does it make Section 3.5 Projectile M