### Wednesday September 20 th

```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
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