VectorsPhysics Book Sections 1.5-

1.8

Two Types of QuantitiesSCALAR• Number with Units

(MAGNITUDE or size)

• Quantities such as time, mass, temperature.• Ex: They traveled 30

miles.(Distance)

VECTOR• Number with Units

(MAGNITUDE or size)• Plus DIRECTION!• Quantities such as velocity,

acceleration, force.• Ex: They traveled 30 miles

due east.(Displacement)

INTRODUCING “VECTOR”

• http://youtu.be/A05n32Bl0aY

NOTATION• Represented in diagrams by arrows.• Direction of arrow = Direction of vector• Length of arrow indicates the magnitude of the vector

•Written in bold with arrows above them. • Ex: m, due east

• To write about just the magnitude (scalar) of the vector, we use italics and no arrows.• Ex: m or “the magnitude of A is 750 m”

Adding Vectors – Same Direction

•The simplest case is when the vectors have the same direction.• In this case ONLY, you can add the magnitudes and keep the direction.•Ex: m, due east and m, due east.

m, due east.

Adding Vectors – Opposite Direction

•Another simple case is when the vectors have the exact opposite direction.• In this case, you can subtract the magnitudes

and use the direction of the vector with the larger magnitude. (similar to adding integers with opposite signs!)•Ex: m, due west and m, due east.• m, due west.

Adding Vectors MathematicallyYou Try:1. cm, due south and cm, due south. Find .• cm, due south2. cm, due south and cm, due north. Find .• cm, due north

Adding Vectors Graphically•When we add vectors together, the result is called a resultant vector.•There are 2 methods for drawing resultant vectors in

diagrams.• Tip to Tail Method – AKA Triangle Method• Parallelogram Method•You may use whichever method makes more sense

to you!

Adding Vectors – Tip to Tail Method1. Draw one vector2. Draw the second vector, beginning at the end of the first.3. Draw the resultant vector stretching from the beginning of the first to the end of the second vector.

Adding Vectors – Parallelogram Method

1. Draw both vectors with a common starting point.2. Make a parallelogram by drawing 2 more sides.3. Draw the resultant vector stretching from the starting point to the farthest corner of the parallelogram.

Adding Perpendicular Vectors•When two vectors are perpendicular to each other, the resultant vector will be the hypotenuse of a right triangle.•We will use the Pythagorean Theorem and Trigonometry to find the magnitude and direction of the resultant vector.

Adding Perpendicular Vectors•Ex: m, due east and m, due north.1. Magnitude: Pythagorean Theorem• so m2. Direction: Trigonometry• so • m, north of east

Vector Components•Sometime we know a vector and it can help to break it into it’s vertical (y) and horizontal (x) components.• Ex: You know how far northwest someone traveled,

but you want to know how far north and how far west.

•We can resolve the vector into its components using trigonometry.

Vector Components•Ex: m and points at an angle of relative to

the y axis. Find the x and y components of this vector.• so m• so m•Check to make sure your answers make sense!

Vector Components Shortcut•To find the vertical and horizontal components of a vector, you will always multiply the hypotenuse by the sine and cosine of the angle.•USUALLY the angles in our diagrams are measures from the x axis• If this is the case, then sin will find the y

component and cos will find the x component.

Vector ComponentsYou try: km and points at an angle of relative to the x axis. Find the x and y components of this vector.

km, km

Problem Solving #1

Problem Solving #2

Problem Solving #3

Problem Solving #4