Motion in Two Dimensions Vectors vector 12 R

Motion in Two Dimensions: Vectors vector 12 R A quantity with both a number and a direction resultant The sum of two or more vectors Properties of Vectors • Vectors can be moved parallel in diagrams • Vectors can be added in any order • Subtract vectors by adding their opposite – If you walk 300 m East then turn around and walk 300 m West, it can also be written as -300 m East. In either case you are back at your starting point. • Multiplying or dividing vectors by scalars results in vectors

Motion in Two Dimensions: Vectors 12 R Adding vectors graphically: • Draw the situation to scale on paper • Draw the resultant as an arrow connecting the starting point and ending point • magnitude is determined using a ruler and multiplying by whatever scale was used • direction is determined using a protractor to measure angle with respect to the first vector

Motion in Two Dimensions: Vectors 12 R Ex:

Motion in Two Dimensions: Vectors 12 R Adding vectors using coordinates: • The Pythagorean theorem (a 2 + b 2 = c 2)can be used when adding vectors as long as they are at right angles to one another • In physics it is useful to think about this as Δx 2 + Δy 2 = (resultant magnitude)2 • Use the tangent function to find the direction of the resultant o tanϴ = opp/adj o ϴ = tan -1(opp/adj)

Motion in Two Dimensions: Vectors 12 R Ex: An archaeologist climbs the Great Pyramid in Giza, Egypt. The height of the pyramid is 136 m and its width is 2. 30 x 102. what is the magnitude and direction of the displacement of the archaeologist after she has climbed from the bottom of the pyramid to the top?

12 L Vectors Practice 1. A Pokemon Go trainer walks 80. m east to catch an Abra (who runs away), she then turns around and walks 30. m west to catch a Sandshrew. Then a Dragonite appears so she turns around and walks 120 m. east and catches it. a. what is the total distance she travelled? b. what is her displacement? 2. While following the directions on his treasure map a pirate walks 45. 0 m north and then turns and walks 7. 5 m east. What is his displacement? 3. Jesus passes a soccer ball 6. 0 m directly across the field to his team mate Alex then kicks the ball straight down the field 15 m to Jesse. What is the ball’s total displacement? 4. A humming bird 3. 4 m above the ground flies 1. 2 m in a straight line. It then drops 1. 4 m to hover above a flower. What is the bird’s total displacement?