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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 1 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 3 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 4