Sample Math Vector Addition.notebook
October 20, 2011
Sample problem using mathematical addition of vectors
THE PROBLEM: Add the following three vectors and find the resultant vector.
Vector A = 4.5 m/s @ 192o
Vector B = 6.8 m/s @ 47o
Vector C = 8.2 m/s @ 324o
STEP #1 Determine the quadrant of each vector. Vector A = 4.5 m/s @ 192o Quadrant #3 ­x component ­y component
Vector B = 6.8 m/s @ 47o Quadrant #1 +x component +y component
Vector C = 8.2 m/s @ 324o Quadrant #2 ­x component +y component
STEP #2 Convert the navigational angles into theta θ angles
o
o
o
θA = 270 ­ 192 = 78
o
o
o
θB = 90 ­ 47 = 43
o
o
o
θC = 324 ­ 270 = 54
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Sample Math Vector Addition.notebook
October 20, 2011
STEP #3 Find the x and y components of vectors A, B, & C
Vector
x components y components
A
(4.5 m/s)(Cos 78o) = ­0.94 m/s (4.5 m/s)(Sin 78o) = ­4.4 m/s
B
(6.8 m/s)(Cos 43o) = +4.97 m/s (6.8 m/s)(Sin 43o) = +4.64 m/s
C
(8.2 m/s)(Cos 54o) = +4.82 m/s (8.2 m/s)(Sin 54o) = +6.63 m/s
x component of the resultant = ­0.79 m/s
y component of the resultant = +6.87 m/s
From this information, we know that the resultant is in quadrant #2 ­x and +y 2
Sample Math Vector Addition.notebook
October 20, 2011
STEP #4 Use the Pythagorean Theorem to calculate the magnitude of the resultant vector.
+6.87 m/s
+6.87 m/s
+6.87 m/s
­0.79 m/s
­0.79 m/s
­0.79 m/s
Resultant Magnitude = √(-0.792) + (+6.872) = 6.92 m/s
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Sample Math Vector Addition.notebook
October 20, 2011
STEP #5 Find the navigational angle of the resultant.
θresultant =
Tan­1 y component
­1 6.78
Tan
=
x component
­0.79
= 83.4o
Remember that the resultant is in quadrant #2!..... so...
NAVresultant = 270o + θresulyant = 353o
Put it all together and resultant vector is...
6.82 m/s @ 353o
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