# Chapter 3: Two â€“ Dimensional Motion and Vectors

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### Transcript of Chapter 3: Two â€“ Dimensional Motion and Vectors

Chapter 3: Two Dimensional Motion and VectorsSection 3-1 and 3-2pages 84-97

VectorsA scalar is a quantity that does not involve direction.55 mph18 cm longA vector is a quantity that involves both magnitude and direction (velocity, acceleration, displacement, force) 55 mph northA downward force of 3 Newtons

Definition Magnitude R is representedby length

Direction is representedby the angle

TailHeadThe resultant vector can be defined in polar coordinates as R at N of E.Try YOURS!!

Parallel Vector Addition1013Adding vectors in the same direction=23 (resultant)Adding vectors in the opposite direction58= 3 (resultant)

Basic Trig FunctionsB = oppA = adjR= hypxyFor the right triangle placed at the origin90oSin = B/R = opp/hypCos = A/R = adj/hypTan = B/A = opp/adjA2 + B2 = R2

Perpendicular Vector Addition512512RR2 = 52 + 122R = 13 = tan-1 5/12 = 22.6o For two perpendicular vectorsConstruct resultant R by drawing a vector from the tail of the horizontal vector to head of the vertical vector

Example:8.00 m/s E5.00 m/s NA boat heads east at 8.00 m/s across a river flowing north at 5.00 m/s. What is the resultant velocity of the boat?R = 9.43 m/s at 321) Use pythagorean theory.2) Use tan = opp/hyp

Multiple Vector AdditionA + B + C + D + E = DistanceR = Resultant = DisplacementCan be added in any order!!

Adding Vectors SUMMARYThe sum of two or more vectors is known as theRESULTANTVectors Acting in the Same Direction (parallel) ADDVectors Acting in the Opposite Direction (parallel) SUBTRACT

At 90o angles Ah- Trigonometry. . . (perpendicular) PYTHAGOREANTAN

At angles other than 90o - three methodsGraphical scaled drawingResolution into Components Method break each vector into right triangles then use trig functionsLaw of Sines and Cosinesc2 = a2 + b2 2abcosC

a = b = csin A sin B sin C

Using the Graphical Method of Vector Addition:Vectors are drawn to scale and the resultant is determined using a ruler and protractor.Vectors are added by drawing the tail of the second vector at the head of the first (tip to tail method).The order of addition does not matter.The resultant is always drawn from the tail of the first to the head of the last vector.

BE METICULOUS IN YOUR DRAWING!!! Your accuracy depends on it. (2, 0.2 cm)

Method 1: Adding Vectors Graphically (Its making a scaled drawing.)

Steps: Decide what quadrant the vectors will be in. Draw the axis and write the in a box.Draw the first vector to scale starting at the origin and label it .Draw the remaining vectors, so that they make a path and label them _____, ______, _____, etc.Draw the as the dashed line from the and label it . Measure the length of ____ to get the and the angle of (from the closest axis) to get the and write your answer in a box.

DIRECTION ALWAYS < 45 angle of .SCALEABCDRESULTANTTAIL OF 1ST VECTOR TO HEAD OF LASTRRMAGNITUDEDIRECTIONRTAIL TO HEAD

Example:Cartman gets upset with Kenny for taking his doughnut. Cartman chases Kenny 30 meters at 40o N of E and then 20 meters at 10o E of N. Calculate Cartmanss total displacement. Solve this graphically.

Example:Cartman gets upset with Kenny for taking his doughnut. Cartman chases Kenny 30 meters at 40o N of E and then 20 meters at 10o E of N. Calculate Cartmanss total displacement. Solve this graphically.

Advantages and Disadvantages of the Graphical MethodCan add any number of vectors at onceUses simple toolsNo mathematical equations needed

Must be correctly draw to scale and at appropriate anglesSubject to human errorTime consuming

This completes Method One!So lets get

Vector problems #1 and #2 due tomorrow.

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