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Ch3sec2

# Ch3sec2 - Objectives Identify appropriate coordinate...

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Objectives Identify appropriate coordinate systems for solving problems with vectors. Apply the Pythagorean theorem and tangent function to calculate the magnitude and direction of a resultant vector. Resolve vectors into components using the sine and cosine functions. Add vectors that are not perpendicular.

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Adding Vectors Mathematically The Pythagorean Theorem 2 2 2 c a b = + 2 2 2 (hypotenuse) (leg 1) (leg 2) = + The Tangent Function opposite leg tangent of angle = adjacent leg θ

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Copyright © by Holt, Rinehart and Winston. All rights reserved. Add. v = 380 km/h, North v 1 v 2 v r θ 2 2 (380 km/h) (145 km/h) r v = + v r = 410 km/h @ 21 ° E of N (or 69 ° N of E) -1 o 145 km tan 21 380 km θ = = 410 km/h r v = 2 2 2 1 2 r v v v = + 2 1 tan v v θ = 2 2 1 2 r v v v = + 1 2 1 tan v v θ - =
Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem Finding Resultant Magnitude and Direction An archaeologist climbs the Great Pyramid in Giza, Egypt. The pyramid’s height is 136 m and its width is 2.30 × 10 2 m. What is the magnitude and the direction of the displacement of the archaeologist after she has climbed from the bottom of the pyramid to the top?

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