Vectors and Two Dimensional Motion

Chapter 3

Scalars vs. VectorsVectors indicate direction ; scalars do not.

Scalar – magnitude with no direction

Vector – magnitude AND direction

Examples :Scalar – Speed, volume, and # of pages

in a book.

Vector – displacement, velocity, and acceleration.

Vectors can be added graphically

Vectors must have same units and describe similar quantities.

The answer found when adding vectors is called the _______________.

Properties of Vectors

Triangle method of additionFigure 3-3

Vectors can be added in any orderFigure 3-4

Section 2Vector Operations

Chapter 3Two Dimensional Motion

Coordinate System in Two DimensionsPositive Y NorthPositive X East

Determining Resultant, Magnitude, and Direction

To find direction Tangent Function *We use tangent function to find the

direction of the resultant. To find magnitude

Pythagorean Theorem*Pythagorean Theorem is ONLY for Right

Triangles.

Pythagorean TheoremFormula c2 = a2 + b2

C = Length of HypotenuseA = Length of LegB = Length of Leg

Only used with Right Triangles!!

Inverse Tangent Function

Guided PracticeSample Problem 3A pg. 90

Resolving Vectors into Components.Vector Components –

horizontal and vertical parts of a displacement/ can be ( ) or ( ) numbers with units.

Ex: x component – parallel to __ _____

y component – parallel to __ _____

***To solve for Vector Components we use Sine and Cosine Functions***

Sine Θ = opposite leg/hypotenuse

Cosine Θ = adjacent leg/ hypotenuse

SOHCAHTOA !!!

Open your books to page 93 Sample 3B

Adding Vectors that are NOT Perpendicular

- Up until now, the vector addition problems we have worked on have been perpendicular.

- In order to work problems like these, we must break our vector into components and use our formulas for magnitude and direction.

Adding Vectors Algebraically1. Select a coordinate system and draw the

vectors to be added/be sure to label each vector

2. Find the X and Y components of all vectors.

3. Find X and Y components of total displacement.

4. Use Pythagorean Theorem to find magnitude of resultant vector.

5. Use trigonometric function to find the the resultant angle with respect to the x axis.

Chapter 3Section 3-3

Projectile Motion

Projectile MotionProjectile Motion is a two dimensional

motion under the influence of gravity.

Objects thrown or launched into the air are subject to gravity are called projectiles.

Ex: softballs, footballs, arrows that are thrown

Remember we talked about Free Fall.Projectile motion is free fall with an INITIAL

Horizontal Velocity…. AND it stays CONSTANT!

Projectiles Follow Parabolic PathThe path of a

projectile is a curve called a parabola.

Neglecting air resistance, a projectile has a Constant horizontal velocity and a Constant free fall acceleration.

There are two types of projectile problems.Projectiles launched horizontallyProjectiles launched at an angle

To calculate vertical and horizontal components, we use the following formulas…

Launched Horizontally

Horizontal Component (Vx)- displacement = horizontal component x time

Δx = vx Δt

Vertical Component (Vy)

Δy = 1/2g(Δt)2

vy,f = gΔt vy,f 2 = 2gΔy