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Vector Addition

Vector Addition. 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

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Vector Addition

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  1. Vector Addition

  2. 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.

  3. Add These Vectors by Drawing • 3 cm @ 90° + 6 cm @ 0° =? resultant (answer vector)

  4. 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)

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

  6. 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.

  7. 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”

  8. SOH-CAH-TOA hypotenuse opposite adjacent θ

  9. Angles • Angles are measured from the +x-axis y Your calculator will give you the angle to the closest part of the x-axis. You need to add or subtract to adjust the angle to the ranges shown. Quadrant 2: 90°-180° Quadrant 1: 0°-90° x Quadrant 3: 180°-270° Quadrant 4: 270°-360°

  10. Example: Magnitude A hiker hikes 22 km East, then 11 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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