Transcript Motion in Two Dimensions - Lompoc Unified School District

Motion in Two Dimensions
Example
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What is the displacement of a person who
walks 10.0 km (E) and then 5.00 km (N) ?
D1 + D 2 = D R
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
a 2 + b2 = c 2
10.02 + 5.002 = c2
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 = 5/11.2
θ = 27°
Final answer 11.2 km (27º N of E)
Vectors by Components
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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
Example
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What are the components of 50 km (47º N
of E)?
Single vector has a vertical and horizontal
component – vx and vy
50km
vx
vy
Example
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A mail carrier leaves the post office and
drives 22.0 km (N), then 47 km (60º S of
E). What is the displacement?
Step 1
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Resolve the angled vector into its two
components
Step 2
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Total the vertical and horizontal
components
Step 3
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Draw the vector from the vertical and
horizontal totals
Step 4
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Solve as a right triangle vector