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Vector Addition

Vector Addition. 9/5 – A Day. Take your homework out and have it on your desk. You will need calculators today. If you do not have your own, grab one from the box near the door. Make sure you picked up the copies from the front as well. . Adding Multiple Vectors by Drawing.

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Vector Addition

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  1. Vector Addition

  2. 9/5 – A Day • Take your homework out and have it on your desk. • You will need calculators today. If you do not have your own, grab one from the box near the door. • Make sure you picked up the copies from the front as well.

  3. Adding Multiple Vectors by Drawing • To add vectors you place the base of the second vector on the tip of the first vector • You make a path out of the arrows like you’re drawing a treasure map • The answer vector (called the resultant) is the vector that connects the start of the path to the end of the path. • Measure the resultant with a ruler to find the magnitude.

  4. Add These Vectors by Drawing • 3 cm @ 90°, 6 cm @ 0° resultant (answer vector)

  5. Tip-to-Tail • This method of adding vectors is called the “Tip-to-tail method” since you put the tail of the second vector on the tip of the first vector resultant (answer vector)

  6. Adding Vectors Mathematically • When adding perpendicular vectors you use the Pythagorean Theorem a b c

  7. Finding the Direction • When adding vectors by drawing you use a protractor and measure the angle of the resultant. • When adding vectors mathematically you use Trigonometry to find the direction of the resultant.

  8. Trig Functions • Sine (sin) • Cosine (cos) • Tangent (tan) • Each function uses two sides of a right triangle • The angle we are using is labeled with the Greek letter “theta” or “θ”

  9. SOH-CAH-TOA θ

  10. Example: Magnitude A hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement. resultant 11 km θ 22 km

  11. Example: Direction A hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement. resultant 11 km θ 22 km Your calculator must be in degrees mode!

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