1. Vectors

2. A vector is a quantity and direction of a variable, such as; displacement, velocity, acceleration and force. A vector is represented graphically as an arrow. The length represents the magnitude (quantity) of the vector, the angle shows the direction.

3. Vectors can be multiplied or divided by a scalar. If A = 5 m A scalar is a value with no direction then 2A is: (10 m)

4. Vectors can be added to find the “net” resultant A B Connect vectors “tip to tail” A + B

5. To find the magnitude of the resultant vector, use the Pythagorean Theorem a 2 + b 2 = c 2 To find the direction of the vector, use trig. functions tan  = opp/adj sin  = opp/hyp cos  = adj/hyp

6. 6 m/s 2 1.5 m/s 2 magnitude: c 2 = a 2 + b 2 = (6 m/s 2 ) 2 + (1.5 m/s 2 ) 2 c = 6.18 m/s 2 direction: tan  = opp/adj = 1.5 m/s 2 / 6 m/s 2 =.25  = tan -1 (.25) = 14° 

7. Measure all directions from the positive x-axis If no logical “x-axis” exists, explain your coordinate system. (i.e.: 20° ahead of down the field)

8. A vector can be broken down into its x and y components 38 ° x comp y comp 5 m cos 38 ° = x comp / 5 m x = (5 m) cos38°= 3.94 m y = (5 m) sin38° = 3.08 m

9. You can add vectors that are not perpendicular by adding their x and y components to make a right triangle, and find the resultant

10. 5 m 75 ° 25 ° x = 5 m(cos 75°) + 4 m(cos 25°) 4 m = 4.92 m 4.92 m y = 5 m(sin75°) + 4 m(sin25°)= 6.52 m 6.52 m magnitude 2 = (4.92 m) 2 + (6.52 m) 2 mag = 8.17 m direction: tan  = 6.52/4.92  = 53°

11. Find the resultant vector’s magnitude and direction 29 ° 5 N 19 ° 7.5 N 3 N