1. Motion in Two Dimensions

2. Example What is the displacement of a person who walks 10.0 km (E) and then 5.00 km (N) ? D 1 + D 2 = D R Use a “tip to tail” method Draw 1 st vector (D 1 ) Draw 2 nd vector (D 2 ) placing its tail at the tip of the 1 st vector

3. Draw the arrow from the tail of the 1 st vector to the tip of the second. This is the resultant vector (sum of two vectors) - D R The magnitude of D R is not equal to the sum of D 1 and D 2 If the two are not in the same direction the resultant is always smaller - D 1 + D 2 > D R - D R least if vectors are in opposite directions - D R most if vectors are in same directions It is not important what order they are added in

4. Method 1 for finding D R Draw vectors to scale and actually measure the result 10 km 5 km D R =

5. Method 2 for finding D R Once the diagram is complete, solve for D R using the Pythagorean theorem a 2 + b 2 = c 2 10.0 2 + 5.00 2 = c 2 c = 11.2 km

6. Must also include the direction Solve for direction of travel using trig identities Sin θ = opp/hyp cos θ = adj/hyp Sin θ = 5/11.2 θ = 27° Final answer 11.2 km (27º N of E)

7. Example Find the displacement of a car that travels 250 km west, 100 km north, 25 km south, and then 190 km east.