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Published byHorace Neal Modified about 1 year ago

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Adding Vectors that are not perpendicular Holt Physics Chapter 3 Section 2 (continued)

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Non-perpendicular vectors Because vectors do not always form right triangles, you cannot automatically apply the Pythagorean theorem and tangent function to the original vectors Resultant vector Vector 1 Vector 2 No right triangle!

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Non-perpendicular vectors This will require new “old” variables For Displacement Vectors Vector #1 Vector #2 Resultant Δx 1 Δx 2 Δx T Δy 1 Δy 2 Δy T D R1 D R2 D RT θ 1 θ 2 θ R

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Non-perpendicular vectors Step #1 You must resolve vector #1 into x & y components Vector 1 Δx 1 Δy 1 D R1 θ1θ1

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Non-perpendicular vectors Step #2 You must resolve vector #2 into x & y components Vector 2 Δx 2 Δy 2 D R2 θ2θ2

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Non-perpendicular vectors Step #3 Add all X components to find Δx T Δx 1 + Δx 2 = Δx T Δx 1 Δx 2 Δx T

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Non-perpendicular vectors Step #4 Add all Y components to find Δy T Δy 1 + Δy 2 = Δy T Δy 1 Δy 2 Δy T

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Non-perpendicular vectors Step #5 Now you have total x & y components Use Pythagorean theorem to find resultant D RT 2 = Δx T 2 + Δy T 2 Δx T Δy T D RT θRθR

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Non-perpendicular vectors Step #6 Use tangent to find the angle - Same equations - Tan θ R = Δy T θ R = Tan -1 (Δy T / Δx T ) Δx T

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Non-perpendicular vectors Resultant vector Vector 1 Vector 2 You may wish to draw the x-total and y-total vectors into the original drawing if it helps you, or make a new triangle with just the totals. Δx T Δy T D RT θRθR

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Non-perpendicular vectors * If you have velocities instead of displacement: Replace “Δ” and “D” with “V” * If you have more than two vectors, the third vector’s variables will be “Δx 3, ….”, and so on.

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