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Motion in Two Dimensions
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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
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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 It is not important what order they are added in
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Once the diagram is complete, solve for DR using the Pythagorean theorem
a2 + b2 = c2 = c c = 11.2 km
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Solve for direction of travel using trig identities
Sin θ = opp/hyp cos θ = adj/hyp Sin θ = 5/ θ = 27° Final answer 11.2 km (27º N of E)
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Vectors by Components Tip to tail method will not be sufficient if the triangle formed is not a right triangle A single angled vector can be expressed as two components Finding the components is called Resolution of the vector
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Example What are the components of 50 km (47º N of E)?
Single vector has a vertical and horizontal component – vx and vy 50km vy vx
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Example A mail carrier leaves the post office and drives 22.0 km (N), then 47 km (60º S of E). What is the displacement?
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Step 1 Resolve the angled vector into its two components
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Step 2 Total the vertical and horizontal components
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Step 3 Draw the vector from the vertical and horizontal totals
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Step 4 Solve as a right triangle vector
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