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Vectors and Two-Dimensional Motion: Scalars vs. Vectors, Properties, and Projectile Motion

This chapter explains the difference between scalars and vectors, the properties of vectors, and how to add vectors algebraically. It also covers projectile motion and the calculations of vertical and horizontal components.

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Vectors and Two-Dimensional Motion: Scalars vs. Vectors, Properties, and Projectile Motion

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  1. Chapter 3 Vectors and Two Dimensional Motion

  2. 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.

  3. Vectors can be added graphically • Vectors must have same units and describe similar quantities. • The answer found when adding vectors is called the _______________.

  4. Properties of Vectors • Triangle method of addition • Figure 3-3 • Vectors can be added in any order • Figure 3-4

  5. Chapter 3Two Dimensional Motion Section 2 Vector Operations

  6. Coordinate System in Two Dimensions • Positive Y  North • Positive X  East

  7. 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.

  8. Pythagorean Theorem • Formula  c2 = a2 + b2 • C = Length of Hypotenuse • A = Length of Leg • B = Length of Leg • Only used with Right Triangles!!

  9. Inverse Tangent Function

  10. Guided Practice • Sample Problem 3A pg. 90

  11. 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

  12. 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.

  13. 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 the resultant angle with respect to the x axis.

  14. Chapter 3 Section 3-3 Projectile Motion

  15. 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!

  16. Projectiles Follow Parabolic Path • The path of a projectile is a curve called a parabola.

  17. 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…

  18. Launched Horizontally Horizontal Component (Vx) - displacement = horizontal component x time • Δx= vxΔt Vertical Component (Vy) Δy= 1/2g(Δt)2 vy,f= gΔt vy,f2 = 2gΔy

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