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UNIT 2 Two Dimensional Motion And Vectors Wednesday September 20th Independence of Motion 2 TODAY’S AGENDA Wednesday, September 20 Vector Operations Mini-Lesson: More Vector Operations (Independence of Motion) Hw: Complete Practice B Problems (all) UPCOMING… Thurs: Problem Quiz 1 Vectors Mini-Lesson: Projectile Motion @ 0° Fri: Projectile Motion @ any angle Mon: LAB 3: Projectile Motion 2 – Dimensional Motion Two-Dimensional Motion means motion the occurs in both the horizontal and vertical directions. Examples: Playing pool (billiards) Throwing a ball to another person. Each dimension of the motion can obey different equations of motion. 4 Keys to Solving 2-D Problems 1) Resolve ALL vectors into their x- and y-components. 2) Work the problem as two 1-Dimensional problems. Each dimension can obey different equations of motion. 3) Re-combine the results of the two components at the end of the problem. 5 Sample Problem You run in a straight line at a speed of 5.00 m/s in a direction that is 40.0° south of west. Displacement = 750 m @ 40.0° S of W How far west have you traveled in 2.50 minutes? west = 750 m cos(40.0°) = -575 m How far south have you traveled in 2.50 minutes? south = 750 m sin(40.0°) = -482 m 6 Sample Problem A roller coaster car rolls from rest down a 20.0° incline with an acceleration of 5.00 m/s2. down incline = 250 m @ 20.0° below x-axis How far horizontally has the coaster travelled in 10.0 s? horizontal = 250 m cos(20.0°) = 235 m How far vertically has the coaster travelled in 10.0 s? vertical = 250 m sin(20.0°) = -85.5 m 7 Sample Problem A car travels 20.0 km due north and then 35.0 km in a direction 60° west of north. Find the resultant displacement. 4.90 x 104 m @ 51.8 above the –x axis 8 Sample Problem A hiker begins a trip by first walking 25.0 km 45.0° south of east from her base camp. On the second day she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger’s tower. Determine the components of the hiker’s displacements in the first and second days. Fx = 17.7 km Sx = 20.0 km Fy = -17.7 km Sy = 34.6 km 9 Sample Problem Find the magnitude and direction of the displacement from base camp. 4.13 x 103 m @ 24.1° N of E 10 Sample Problem Determine the magnitude and direction of the velocity of a plane that is flying toward 180.0° at 100.0 km/h while the wind blows toward 90.0° at 65.0 km/h. 55.3 m/s @ 33.0° N of W 11 Sample Problem An airplane trip involves three legs, with two stopovers. The first leg is due east for 620 km; the second leg is southeast (45°) for 440 km; and the third leg is at 53.0° south of west for 550 km. What is the plane’s total displacement? 9.60 x 105 m @ 51.3° below the x-axis 12 END 13