Wednesday September 20 th 2 Independence of Motion
TODAY’S AGENDA 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 Wednesday, September 20
2 – Dimensional Motion 4 Two-Dimensional Motion means motion the occurs in both the horizontal and vertical directions. Each dimension of the motion can obey different equations of motion. Examples: Playing pool (billiards) Throwing a ball to another person.
5 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.
6 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. How far west have you traveled in 2.50 minutes? How far south have you traveled in 2.50 minutes? west = 750 m cos(40.0°) = -575 m south = 750 m sin(40.0°) = -482 m Displacement = 750 m @ 40.0° S of W
7 Sample Problem A roller coaster car rolls from rest down a 20.0° incline with an acceleration of 5.00 m/s 2. How far horizontally has the coaster travelled in 10.0 s? How far vertically has the coaster travelled in 10.0 s? horizontal = 250 m cos(20.0°) = 235 m vertical = 250 m sin(20.0°) = -85.5 m down incline = 250 m @ 20.0° below x-axis
8 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 10 4 m @ 51.8 above the –x axis
9 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. F x = 17.7 kmF y = -17.7 km S x = 20.0 kmS y = 34.6 km
10 Sample Problem Find the magnitude and direction of the displacement from base camp. 4.13 x 10 3 m @ 24.1° N of E
11 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
12 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 10 5 m @ 51.3° below the x-axis