# Physics 3 - Physics Chapter 3 Two-Dimensional Motion and...

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Physics Chapter 3: Two-Dimensional Motion and Vectors

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Two-Dimensional Motion and Vectors Scalar and Vector Quantities Scalar Quantity Magnitude (number and units) ex. 15km, 25 0 C Vector Quantity Magnitude and Direction ex. 15km north
Two-Dimensional Motion and Vectors Vectors Represented by Arrows Direction of the Arrow Represents the Direction of the Vector The Length of the Arrow is Proportional to the Magnitude of the Vector

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Two-Dimensional Motion and Vectors Vectors Components Two Perpendicular Components Add to Form Resultant (Displacement) A Vector May be Broken Down Into Its “X” and “Y” Components Resultant Vector Sum of Two or More Vectors
Two-Dimensional Motion and Vectors Vectors Components Vector “r” West Component North Component

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Two-Dimensional Motion and Vectors Vectors Components m m m r r o x 36 . 1 ) 906 . 0 )( 50 . 1 ( 0 . 25 cos = = =
Two-Dimensional Motion and Vectors Vectors Components m m m r r o y 634 . 0 ) 423 . 0 )( 50 . 1 ( 0 . 25 sin = = =

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Two-Dimensional Motion and Vectors Vectors Ex. Height Determination Distance to Cliff = 500’ Angle = 34 o
Two-Dimensional Motion and Vectors Vectors Ex. Height Determination Distance to Cliff = 500’ Angle = 34 o θ tan b h = ft ft x h o 337 34 tan ) 10 5 ( 2 = =

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Two-Dimensional Motion and Vectors Vectors Components Determination of Direction Observe Direction From Tail of Resultant to Right Angle Formed by X and Y Components
Two-Dimensional Motion and Vectors Vectors Determination of Direction

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Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Graphically To add vectors A and B, place the tail of B at the head of A. The sum, C = A+B, is the vector extending from the tail of A to the head of B.

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Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Graphically C = A + B
Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Graphically C = A + B C = B + A

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Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Using Components x x x B A C + = y y y B A C + =
Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Using Components A=5.00m B=4.00m x x x B A C + = y y y B A C + =

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Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Using Components A=5.00m B=4.00m m m A o x 50 . 2 60 cos ) 00 . 5 ( = = m m A o y 33 . 4 60 sin ) 00 . 5 ( = = m m B o x 76 . 3 20 cos ) 00 . 4 ( = = m m B o y 37 . 1 20 sin ) 00 . 4 ( = =
Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Using Components A=5.00m B=4.00m A x =2.50m A y =4.33m B x =3.76m B y =1.37m m m m B A C x x x 26 . 6 76 . 3 50 . 2 = + = + = m m m B A C y y y 70 . 5 37 . 1 33 . 4 = + = + = m m m C C C y x 47 . 8 ) 70 . 5 ( ) 26 . 6 ( 2 2 2 2 = + = + =

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Two-Dimensional Motion and Vectors Adding and Subtracting Vectors Adding Vectors Using Components m m m C
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