VECTORS AND TWO DIMENSIONAL MOTION CHAPTER 3

SCALARS VS. VECTORS Vectors 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 Resultant.

PROPERTIES OF VECTORS Triangle method of addition Figure 3-3 Vectors can be added in any order Figure 3-4

SECTION 2 VECTOR OPERATIONS CHAPTER 3 TWO DIMENSIONAL MOTION

COORDINATE SYSTEM IN TWO DIMENSIONS Positive Y  North Positive X  East

DETERMINING RESULTANT, MAGNITUDE, AND DIRECTION To find Magnitude  Pythagorean Theorem *Pythagorean Theorem is ONLY for Right Triangles. Formula  c 2 = a 2 + b 2 To find Direction  Inverse Tangent Function *We use tangent function to find the direction of the resultant. Formula 

PYTHAGOREAN THEOREM Formula  c 2 = a 2 + b 2 C = Length of Hypotenuse A = Length of Leg B = Length of Leg Only used with Right Triangles!!

INVERSE TANGENT FUNCTION

GUIDED PRACTICE Sample 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 x axis y component – Parallel to y axis 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 ALGEBRAICALLY 1. 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 resultant angle with respect to the x axis.

CHAPTER 3 Section 3-3 Projectile Motion

PROJECTILE MOTION Projectile 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 PATH The 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 horizontally Projectiles 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