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Understanding Vector Components and Trigonometry in Physics: A Comprehensive Review

This material covers essential concepts in vector components, trigonometry, and motion modeling in physics. It reviews how to determine the x- and y-components of vectors, explores vector magnitude and direction, and delves into constant acceleration and velocity models. The content includes example problems and solutions, as well as practice questions to enhance understanding. Key topics such as calculating maximum altitude, flight duration, and creating velocity versus time graphs are also discussed. This resource is designed for students seeking to solidify their grasp of vector analysis.

benjamin-guerra
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Understanding Vector Components and Trigonometry in Physics: A Comprehensive Review

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  1. Physics 151 Week 6 Day 2 Topics Trigonometry Review Vector Components Vector magnitude and direction

  2. General Motion Model

  3. Constant Acceleration and Constant Velocity Model Slide 2-4

  4. Trigonometry and Vector Component Review

  5. Component Vectors and Components Slide 3-22

  6. Checking Understanding What are the x- and y-components of these vectors? 3, 2 2, 3 3, 2 2, 3 3, 2 Slide 3-23

  7. Answer What are the x- and y-components of these vectors? 3, 2 2, 3 3, 2 2, 3 3, 2 Slide 3-24

  8. Checking Understanding What are the x- and y-components of these vectors? 3, 1 3, 4 3, 3 4, 3 3, 4 Slide 3-25

  9. Answer What are the x- and y-components of these vectors? 3, 1 3, 4 3, 3 4, 3 3, 4 Slide 3-26

  10. Checking Understanding The following vectors have length 4.0 units. What are the x- and y-components of these vectors? 3.5, 2.0 2.0, 3.5 3.5, 2.0 2.0, 3.5 3.5, 2.0 Slide 3-29

  11. Answer The following vectors have length 4.0 units. What are the x- and y-components of these vectors? 3.5, 2.0 2.0, 3.5 3.5, 2.0 2.0, 3.5 3.5, 2.0 Slide 3-30

  12. Angle φthat specifies the direction of is given by tan–1(Cy /Cx) tan–1(Cx /|Cy|) tan–1(Cy /|Cx|) tan–1(Cx /Cy) tan–1(|Cx |/|Cy|)

  13. Angle φthat specifies the direction of is given by tan–1(Cy /Cx) tan–1(Cx /|Cy|) tan–1(Cy /|Cx|) tan–1(Cx /Cy) tan–1(|Cx |/|Cy|)

  14. Checking Understanding The following vectors have length 4.0 units. What are the x- and y-components of these vectors? 3.5, 2.0 2.0, 3.5 3.5, 2.0 2.0, 3.5 3.5, 2.0 Slide 3-27

  15. Answer The following vectors have length 4.0 units. What are the x- and y-components of these vectors? 3.5, 2.0 2.0, 3.5 3.5, 2.0 2.0, 3.5 3.5, 2.0 Slide 3-28

  16. Vector Components

  17. Vector Components

  18. Problem 2.64 A 200 kg weather rocket is loaded with 100 kg  of fuel and fired straight up. It accelerates upward at 30.0 m/s2 for 30.0 s, then runs out of fuel. Ignore any air resistance effects. A. What is the rocket’s maximum altitude? B. How long is the rocket in the air? C. Draw a (quantitative) velocity-versus-time graph for the rocket from liftoff until it hits the ground.

  19. Pictorial Diagram Example 2

  20. Exam Tips • Instantaneous velocity • Area under the graph • Algebra in symbols • Givens Required • Complete explanations • Use homework to practice good solutions

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