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Motion in Two Dimensions

Motion in Two Dimensions. 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.

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Motion in Two Dimensions

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  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) ? • 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

  3. 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

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

  5. 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

  6. Must also include the direction • Solve for direction of travel using trig identities • Sin θ = opp/hypcos 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.

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