Vector Addition: Parallelogram Method Jerome walks 4 km north, and 8 km east. What is his displacement?

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Presentation transcript:

Vector Addition: Parallelogram Method Jerome walks 4 km north, and 8 km east. What is his displacement?

Graphical: Tip to Tail Method Jerome walks 4 km north, and 8 km east. What is his displacement?

Graphical Vector Addition: Parallelogram Method

Tip to Tail Method

A B C D R Tip to Tail method

Analytical vector addition 75° 20°

Analytical vector addition 75° 20°

cosθ = a/h a = h cosθ therefore a = h cosθ h = 3km a = 3 cos20 ° a = 2.82km sinθ = o/h o = h sinθ therefore o = h sinθ o = 3 sin20° o = 1.03km

Analytical vector addition 75° 20° Vector addition table VectormagAngle X Comp’t Y Comp’t Res’t

Analytical vector addition Vector addition table VectormagAngle X Comp’t Y Comp’t Res’t R 2 = x 2 + y 2 R 2 = R = 4.46 km 4.46 R

Analytical vector addition Vector addition table VectormagAngle X Comp’t Y Comp’t Res’t tanθ = opp/adj θ = tan -1 (y/x) θ = tan -1 (2.96/3.34) θ = 41.5˚ 4.46 R 41.5˚

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