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Vectors - Finding Vector Components Contents: Definition of vector components

Vectors - Finding Vector Components Contents: Definition of vector components Whiteboards: Writing the notation How to find components Whiteboard Am to VC. A:. Vectors - What components are. Y - Component. X - Component. TOC. A = 4 cm x + 3 cm y (This is how you write it). ^. ^.

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Vectors - Finding Vector Components Contents: Definition of vector components

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

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

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

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

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

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

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

  8. Vectors - Finding Components - step by step 27o 90o 51o 0o Or 360o 180o 17o 270o 15o Step 1: Find the Trig angle – ACW from x axis This is the trig angle T = 360 – 17 = 343o OR T = -17o T= 270 + 51 = 321o T= 270 – 15 = 255o TOC

  9. Whiteboards: Getting the trig angle 1 | 2 | 3 | 4 | 5 | 6 TOC

  10. 90 – 32 = 58o What’s the Trigonometric angle? 32o W 58o

  11. 180 + 38 = 218o What’s the Trigonometric angle? 38o W 218o

  12. 270 - 13 = 257o What’s the Trigonometric angle? 13o W 257o

  13. 180 - 22 = 158o What’s the Trigonometric angle? 22o W 158o

  14. 90 + 26 = 116o What’s the Trigonometric angle? 26o W 116o

  15. 360 - 42 = 318o What’s the Trigonometric angle? 42o W 318o

  16. 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) TOC

  17. 12 m 27o Vectors - Finding Components - step by step  = 180o – 27o = 153o x = (12 m)Cos(153o) = -10.692 m y = (12 m)Sin(153o) = +5.448 m Step 2: Figure the sides using Cos and Sin: x = mag Cos() y = mag Sin() (iff  = trig angle) TOC

  18. 12 m 27o Vectors - Finding Components - step by step Step 3: Write it in Vector Component notation: • Vector = -11 m x + 5.4 m y (With sig figs) • Reality Check: • (+ and -), • relative size TOC

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

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

  21. 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 W 22.8 km x + 14.4 km y

  22. 27o 42 m  = 360 – 27 = 333o 42cos(333) x + 42sin(333) y 37.42227402 -19.06760099 37 m x + -19 m y W 37 m x + -19 m y

  23. 77o 5.0 feet  = 90 + 77 = 167o 5cos(167) x + 5sin(167) y -4.871850324 1.124755272 -4.9 ft x + 1.1 ft y W -4.9 ft x + 1.1 ft y

  24. 38o 110.0 N  = 270 + 38 = 308o 110.0cos(308) x + 110.0sin(308) y 67.72276229 -86.681182968 N x + -87 N y W 68 N x + -87 N y

  25. 30.0o 5.0 m/s  = 180 + 30.0 = 210.0o 5.0cos(210.0) x + 5.0sin(210) y -4.330127019 -2.5 -4.3 m/s x + -2.5 m/s y W -4.3 m/s x + -2.5 m/s y

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