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# 1 - vectors notes

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Vector foundation for my AP class

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### 1 - vectors notes

1. 1. Vector vs. ScalarVector Ex. Force  magnitude & direction Weight (amount) VelocityScalar Acceleration  magnitude Ex. Mass Time Money Distance
2. 2. Vector logisticsVectors are represented by an arrow Tells direction Length tells magnitudeCoordinate axis are used to represent position North 10 N @ 45 +y 90° 180° +xWest -x East 0° 270° -y SouthVectors are the same no matter where they are located, as longas the magnitude and direction are the same!
3. 3. Resultant  a single vector that replaces two or more vectors1. Adding vectors A = 5.00 N @ 0.00° 5 B = 7.00 N @ 0.00° 7 R = 12.0 N @ 0.00°2. Subtracting vectors A = 5.00 N @ 0.00° (special case of addition) B = 7.00 N @ 180° 5 7A + B = 5 + -7 = -2 or R = 2.00 N @ 180°
4. 4. 3. Adding at 90 A = 7.00 N @ 0.00° B = 5.00 N @ 90.0° Remember: Resultant is from beginning to end! 5 7How do you draw this?Parallelogram.Draw dotted lines parallel to 5original vectors.Draw resultant from solid 7lines to dotted lines.
5. 5. How do you calculate the resultant?Magnitude  Pythagorean theorem 5Direction  SOHCAHTOA 2 2 opp 7R 5 7 8.60N tan adj thetaIs the angle in  first 5reference to the tan 1 insideorigin? If not, add 7 angle youback to 0. 35.5 come to from 0
6. 6. yt. M = 54.0 N @ 10.0° O = 35.0 N @ 100° R 35 2 2 54 R 54 35 64.4N Steps: opptan 1. adj 35 2. draw a picture 1 tan 54 3. pythagorean theorem 32.9 +10 = 42.9° 4. inverse tangent 5. add angle back to zero
7. 7. ComponentsComponents  2 vectors that replace 1 vector 1 is always on the x – axis M My 1 is always on the y – axis A Mx Ay yt Px Cx Py P Ax C Cy Components are always at right angles. Components are independent of each other!
8. 8. A = 87.0 m/s @ 40.0How do you mathematically find Ay & Ax? opp SOHCAHTOA cos adj sin adj hypSet angle theta. cos 40 Ax sin(40) Ay 87 87 Ax 87 cos 40 Ay 87 sin(40) A Ay When finding components, it will always be this way! Ax = mag cos (angle) Ax Ay = mag sin (angle) y sin, because x is cos
9. 9. Vectors: 90°To add vectors that are not at 90° to each other, the vectors must first be broken into their components.ex. A = 10.4 m/s @ 75° B = 6.7 m/s @ 25° R Ay A B By Ax Bx
10. 10. Steps:1. components  find xtot & ytot2. draw a picture3. pythagorean theorem4. inverse tangent5. add angle back to zero
11. 11. ex. A = 10.4 m/s @ 75° B = 6.7 m/s @ 25°Ax = 10.4 cos 75 = 2.69 Ay = 10.4 sin 75 = 10.0Bx = 6.7 cos 25 = 6.07 By = 6.7 sin 25 = 2.83 xtot = 8.76 ytot = 12.83 ytot = 12.83 R= (8.762 + 12.832) R R = 15.5 θ = tan-1 (12.83/8.76) θ = 55.9° θ R = 15.5 m/s at 55.9° Xtot = 8.76