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Tecnología
1 de 93
How to Use This Presentation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Chapter Presentation Transparencies Sample Problems Visual Concepts Standardized Test Prep Resources
Table of Contents ,[object Object],[object Object],[object Object],[object Object],Two-Dimensional Motion and Vectors Chapter 3
Objectives ,[object Object],[object Object],[object Object],Section 1 Introduction to Vectors Chapter 3
Scalars and Vectors ,[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 1 Introduction to Vectors
Scalars and Vectors Chapter 3 Section 1 Introduction to Vectors
Graphical Addition of Vectors ,[object Object],[object Object],Chapter 3 Section 1 Introduction to Vectors A student walks from his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.
Triangle Method of Addition ,[object Object],[object Object],[object Object],Chapter 3 Section 1 Introduction to Vectors
Triangle Method of Addition Chapter 3 Section 1 Introduction to Vectors
Properties of Vectors ,[object Object],[object Object],[object Object],Chapter 3 Section 1 Introduction to Vectors
Properties of Vectors Chapter 3 Section 1 Introduction to Vectors
Subtraction of Vectors Chapter 3 Section 1 Introduction to Vectors
Multiplication of a Vector by a Scalar Chapter 3 Section 1 Introduction to Vectors
Objectives ,[object Object],[object Object],[object Object],[object Object],Section 2 Vector Operations Chapter 3
Coordinate Systems in Two Dimensions ,[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Determining Resultant Magnitude and Direction ,[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Determining Resultant Magnitude and Direction, continued ,[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Determining Resultant Magnitude and Direction, continued ,[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Sample Problem ,[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Sample Problem, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Sample Problem, continued ,[object Object],Chapter 3 Section 2 Vector Operations 2. Plan Choose an equation or situation: The Pythagorean theorem can be used to find the magnitude of the archaeologist’s displacement. The direction of the displacement can be found by using the inverse tangent function.
Sample Problem, continued Chapter 3 Section 2 Vector Operations 3. Calculate ,[object Object],[object Object]
Resolving Vectors into Components ,[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Resolving Vectors into Components, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Resolving Vectors into Components, continued ,[object Object],[object Object],Chapter 3 Section 2 Vector Operations
Resolving Vectors Chapter 3 Section 2 Vector Operations
Adding Vectors That Are Not Perpendicular Chapter 3 Section 2 Vector Operations ,[object Object],[object Object],d 2 d 1
Adding Vectors That Are Not Perpendicular, continued Chapter 3 Section 2 Vector Operations ,[object Object],[object Object],As shown in the figure, these sums will be the two perpendicular components of the resultant, d. The resultant’s magnitude can then be found by using the Pythagorean theorem, and its direction can be found by using the inverse tangent function.
Adding Vectors That Are Not Perpendicular Chapter 3 Section 2 Vector Operations
Sample Problem ,[object Object],[object Object],Chapter 3 Section 2 Vector Operations
[object Object],Chapter 3 Section 2 Vector Operations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Sample Problem, continued
[object Object],Chapter 3 Section 2 Vector Operations Make a separate sketch of the displacements for each day. Use the cosine and sine functions to find the components. Sample Problem, continued
[object Object],Chapter 3 Section 2 Vector Operations 4 . Use the Pythagorean theorem to find the magnitude of the resultant vector. Sample Problem, continued
[object Object],Chapter 3 Section 2 Vector Operations Sample Problem, continued
Objectives ,[object Object],[object Object],[object Object],Section 3 Projectile Motion Chapter 3
Projectiles ,[object Object],[object Object],[object Object],Chapter 3 Section 3 Projectile Motion
Projectiles, continued ,[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 3 Projectile Motion
Projectile Motion Chapter 3 Section 3 Projectile Motion
Kinematic Equations for Projectiles ,[object Object],[object Object],[object Object],Chapter 3 Section 3 Projectile Motion
Kinematic Equations for Projectiles, continued ,[object Object],[object Object],[object Object],Chapter 3 Section 3 Projectile Motion
Kinematic Equations for Projectiles, continued ,[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 3 Projectile Motion ,[object Object],[object Object],[object Object]
Sample Problem ,[object Object],[object Object],Chapter 3 Section 3 Projectile Motion
[object Object],[object Object],Chapter 3 Section 3 Projectile Motion Sample Problem, continued
[object Object],Chapter 3 Section 3 Projectile Motion Sample Problem, continued
Chapter 3 3 . Choose a kinematic equation to solve for time. Rearrange the equation for motion along the x -axis to isolate the unknown  t , which is the time the dart takes to travel the horizontal distance. Section 3 Projectile Motion Sample Problem, continued
Chapter 3 4 . Find out how far each object will fall during this time. Use the free-fall kinematic equation in both cases. For the banana, v i = 0. Thus:  y b = ½ a y (  t ) 2 = ½ (–9.81 m/s 2 )(0.215 s) 2 = –0.227 m ,[object Object],[object Object],[object Object],[object Object],Section 3 Projectile Motion Sample Problem, continued
Chapter 3 5 . Analyze the results. ,[object Object],[object Object],[object Object],The dart hits the banana. The slight difference is due to rounding. Section 3 Projectile Motion ,[object Object],[object Object],Sample Problem, continued
Objectives ,[object Object],[object Object],Section 4 Relative Motion Chapter 3
Frames of Reference ,[object Object],[object Object],[object Object],Chapter 3 Section 4 Relative Motion
Frames of Reference, continued ,[object Object],[object Object],[object Object],Chapter 3 Section 4 Relative Motion
Relative Motion Chapter 3 Section 4 Relative Motion
Relative Velocity ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 4 Relative Motion
Relative Velocity, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 3 Section 4 Relative Motion
Relative Velocity Chapter 3 Section 4 Relative Motion
Multiple Choice ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Multiple Choice, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Short Response ,[object Object],Standardized Test Prep Chapter 3
Short Response ,[object Object],[object Object],Standardized Test Prep Chapter 3
Short Response, continued ,[object Object],Standardized Test Prep Chapter 3
Short Response, continued ,[object Object],[object Object],Standardized Test Prep Chapter 3
Short Response, continued ,[object Object],Standardized Test Prep Chapter 3
Short Response, continued ,[object Object],Standardized Test Prep Chapter 3 Answer: 29.4 m/s
Extended Response ,[object Object],Standardized Test Prep Chapter 3
Extended Response ,[object Object],Standardized Test Prep Chapter 3 Answer: 10.8 m
Extended Response, continued ,[object Object],[object Object],[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Extended Response, continued ,[object Object],[object Object],[object Object],Standardized Test Prep Chapter 3
Extended Response, continued ,[object Object],[object Object],Standardized Test Prep Chapter 3
Graphical Addition of Vectors Chapter 3 Section 1 Introduction to Vectors
Adding Vectors That Are Not Perpendicular Chapter 3 Section 2 Vector Operations
Projectiles Chapter 3 Section 3 Projectile Motion
Frames of Reference Chapter 3 Section 4 Relative Motion

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