UNIT 2Two Dimensional Motion

And Vectors

Wednesday September 20th

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Independence of Motion

TODAY’S AGENDA

Vector OperationsMini-Lesson: More Vector Operations

(Independence of Motion)Hw: Complete Practice B Problems (all)

UPCOMING…

Thurs: Problem Quiz 1 VectorsMini-Lesson: Projectile Motion @ 0°

Fri: Projectile Motion @ any angle Mon: LAB 3: Projectile Motion

Wednesday, September 20

2 – Dimensional Motion

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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.

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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.

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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

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Sample Problem

A roller coaster car rolls from rest down a 20.0° incline with an acceleration of 5.00 m/s2.

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

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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

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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 Fy = -17.7 kmSx = 20.0 km Sy = 34.6 km

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Sample Problem

Find the magnitude and direction of the displacement from base camp.

4.13 x 103 m @ 24.1° N of E

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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

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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

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END