Vectors: Finding Vector Components

Explore the definition of vector components and how to find them. Discover the components of vectors and learn how to write the notation for vector components. Follow along with informative whiteboard illustrations to understand vector components visually. Practice drawing components from the tail to the tip using arrows at various angles. Engage with the content to enhance your understanding of vector components.

• Vectors
• Components
• Notation
• Illustrations
• Mathematics

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Uploaded on Mar 02, 2025 | 0 Views

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Presentation Transcript

1. Vectors - Finding Vector Components Contents: Definition of vector components Whiteboards: Writing the notation How to find components Whiteboard Am to VC

2. Vectors - What components are A: Y - Component X - Component

3. Vectors - What components are Suppose A = 5 cm Ay = 3 cm Ax = 4 cm ^ A = 4 cm x + 3 cm y (This is how you write it) ^

4. Whiteboards: Writing the notation 1 | 2 | 3

5. 3.2 m 4.5 m 4.5 m x + 3.2 m y

6. 3.9 m 1.2 m -1.2 m x + -3.9 m y

7. 4.1 m 1.9 m -1.9 m x + 4.1 m y

8. Whiteboards: Drawing the components 1 | 2 | 3 | 4 | 5 | 6

9. Draw the components from the tail to the tip using arrows 32o

10. Draw the components from the tail to the tip using arrows 38o

11. Draw the components from the tail to the tip using arrows 13o

12. Draw the components from the tail to the tip using arrows 22o

13. Draw the components from the tail to the tip using arrows 26o

14. Draw the components from the tail to the tip using arrows 42o

15. Vectors - Try this yourself Get out your calculator type: sin 90 <ENTER> 1???? If not <2nd?> MODE Cursor arrows to Degree <ENTER> <CLEAR> Try again (sin 90)

16. Vectors - Finding Components - step by step 12 m 27o Step 1: Draw the components Use Arrows/Around angle From tail to tip of vector Step 2: Find the Adj and Opp sides: A = (Hyp)Cos( ) O = (Hyp)Sin( ) Step 3: Write as components: Decide x and y Decide + and Write as ______ m x + ______ m y

17. Vectors - Try this yourself 31.0o 23.0 m/s 1. Draw the Components 2. Figure the components with sin and cos 3. Write the answer in VC Notation = 90 + 31 = 121o 23cos(121) x + 23sin(121) y -11.846 x + 19.715 y -11.8 m/s x + 19.7 m/s y

18. Whiteboards: AM to VC 1 | 2 | 3 | 4 | 5

19. 27.0 km 32.2o = 32.2o 27.0cos(32.2) x + 27.0sin(32.2) y 22.84721549 14.38765945 22.8 km x + 14.4 km y 22.8 km x + 14.4 km y

20. 77o 5.0 feet -5sin(77) x + 5cos(77) y -4.871850324 1.124755272 -4.9 ft x + 1.1 ft y -4.9 ft x + 1.1 ft y

21. 27o 42 m +42cos(27) x + -42cos(27) y 37.42227402 -19.06760099 37 m x + -19 m y 37 m x + -19 m y

22. 38o 110.0 N +110.0sin(38) x + -110.0cos(38) y 67.72276229 68 N x + -87 N y -86.6811829 68 N x + -87 N y

23. 30.0o 5.0 m/s -5.0cos(30) x + -5.0sin(30) y -4.330127019 -4.3 m/s x + -2.5 m/s y -2.5 -4.3 m/s x + -2.5 m/s y