vector addition: parallelogram method jerome walks 4 km north, and 8 km east. what is his...
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Graphical Vector Addition: Parallelogram MethodTRANSCRIPT
Vector Addition: Parallelogram MethodJerome walks 4 km north, and 8 km east. What is his displacement?
Graphical: Tip to Tail MethodJerome walks 4 km north, and 8 km east. What is his displacement?
Graphical Vector Addition:Parallelogram Method
Tip to Tail Method
AB
C
D
R
Tip to Tail method
Analytical vector addition
2km @ 75°
3km @ 20°
Analytical vector addition
2km @ 75°
3km @ 20°
3km @ 20°
cosθ = a/htherefore a = h cosa = h cosθθ
h = 3km
a = 3 cos20a = 3 cos20°°a = 2.82kma = 2.82km
sinθ = o/htherefore o = h sino = h sinθθ
o = 3 sin20°o = 3 sin20°o = 1.03kmo = 1.03km
Analytical vector addition
2km @ 75°
3km @ 20°
Vector addition table Vector mag AngleX
Comp’tY
Comp’t1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
Analytical vector addition
Vector addition table Vector mag AngleX
Comp’tY
Comp’t1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
R2 = x2 + y2
R2 = 3.342 + 2.962
R = 4.46 km4.46
R
Analytical vector addition
Vector addition table Vector mag AngleX
Comp’tY
Comp’t1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
tanθ = opp/adjθ = tan-1(y/x)θ = tan-1(2.96/3.34)θ = 41.5˚ 4.46
R
41.5˚