Motion in Two Dimensions

Example What is the displacement of a person who

walks 10.0 km (E) and then 5.00 km (N) ? D1 + D2 = DR

Use a “tip to tail” method Draw 1st vector (D1)

Draw 2nd vector (D2) placing its tail at the tip of the 1st vector

Draw the arrow from the tail of the 1st vector to the tip of the second. This is the resultant vector (sum of two vectors) - DR

The magnitude of DR is not equal to the sum of D1 and D2

If the two are not in the same direction the resultant is always smaller - D1 + D2 > DR

- DR least if vectors are in opposite directions

- DR most if vectors are in same directions It is not important what order they are added in

Method 1 for finding DR

Draw vectors to scale and actually measure the result

10 km

5 kmDR =

Method 2 for finding DR

Once the diagram is complete, solve for DR using the Pythagorean theorem

a2 + b2 = c2

10.02 + 5.002 = c2 c = 11.2 km

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)

Example Find the displacement of a car that travels

250 km west, 100 km north, 25 km south, and then 190 km east.