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Magnitude

Magnitude. The magnitude of a vector is represented by its length. You can multiply the magnitude of a vector by a scalar quantity to change its length. A = 10m. 2A =20m. 0.5A =5m. Direction. All vectors must have a direction. North, south, east, west Or an angle

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Magnitude

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  1. Magnitude • The magnitude of a vector is represented by its length. • You can multiply the magnitude of a vector by a scalar quantity to change its length. A = 10m 2A =20m 0.5A =5m

  2. Direction • All vectors must have a direction. • North, south, east, west • Or an angle • Sometimes measured from the horizontal or vertical • Sometimes measured from the positive x-axis and around to 360o 230o 30o C = 20m C = 17m B = 15m 40o

  3. ‘Adding’ Vectors • Must manipulate all vectors so they are put “tip to tail” • Resultant points from start to finish. B = 15m A = 10m 40o 30o C = 20m

  4. Sketch the vector sum of A+B • Must manipulate all vectors so they are put “tip to tail” • Resultant points from start to finish. B = 15m 40o A = 10m

  5. Sketch the vector sum of A+B+C • Must manipulate all vectors so they are put “tip to tail” • Resultant points from start to finish. B = 15m 30o C = 20m A = 10m 40o

  6. Sketch the resultant of A-B • Flip the direction of the one being subtracted • Then put tip to tail and follow adding procedure A = 10m B = 15m 40o

  7. Components of Vectors • Every vector will have a… • Horizontal component that points directly left or right • Vertical component that points directly up or down. • The components should be drawn tip to tail and lead to the same point as the original vector. • The angle goes by the start. Vertical component Original vector = 25m Horizontal component

  8. Calculating Vector Components • In this case… • Horizontal component is the adjacent side which can be calculated using • Vertical component is the opposite side which can be calculated using = 25m sin 40o = 16m • REMEMBER: horizontal is not always cosine. It depends where the angle is located! • If the angle is to the vertical, sine and cosine would flip. Vertical component Original vector = 25m Horizontal component

  9. Find the components of the following vectors A = 10m • m B = 15m 30o C = 20m • = 15m sin 40o • = 9.6m 40o • = 20m cos 30o • = 17.3m

  10. Find the magnitude and direction of A+B • Step 1: find the components of each vector • Step 2: add all of the x-components together to find the resultant’s x-component • Step 3: add all of the y-componentstogether to find the resultant’s y-component • Step 4: build your actual resultant out of its components you just fund. • Step 5: use Pythagorean Theorem and SohCahToa to find magnitude and direction of resultant. RESULTANT X-component: 10m+11.5m = 21.5m Y- component: 0m+9.6m = 9.6m c= 15.8m A = 10m • m • = 15m sin 40o • = 9.6m B = 15m • 9.6m 40o

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