6.03 - Adding Subtracting Vectors | Lecture Note

University:
High School
Course:
High School Physics
Academic year:

2024
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6.03 Adding & Subtracting Vectors Recap of Necessary Skills Properties of Angles Vertically Opposite ◼ Alternate Interior ◼ Alternate Exterior ◼ Corresponding ◼ Complementary ◼ Supplementary ◼ 2 1 4 6 5 8 3 7 Cosine Law ◼ B A C Cosine Law ◼ B A C Sine Law ◼ B A C ◼ Vectors can be added or subtracted resulting in another vector ◼ Chasles relation (Tail to Tip):  Given points A, B & C then AB + BC = AC B C A Resultant ◼ Ex Use Chasles relation to find the resultant ◼ Vectors can be added or subtracted resulting in another vector ◼ Parallelogram Method (Tail to Tail):  Given points A, B C & D then AB + AD = AC B C A Resultant D Geometric Approach: Sum of vectors determined by placing end to end (head to tail) ◼ Resultant defined by tail of first vector & head of last vector If subtracting, add the ◼ Ex. ◼ u v v+u opposite vector Ex u −u v v −u ◼ Exam Question Try It ◼ 5 5 2 2 Algebraic Approach: ◼ ◼ Sum of vectors determined by the sum of their components u = (a, b ) u + v = (a + c , b + d v = (c, d ) u − v = (a − c , Ex ) b−d) If u = (2, 3) & v = (− 1, 5) then… u + v = (2 + −1, 3 + 5 ) = (1, 8) u − v = (2 − −1, 3 − 5 ) = (3, − 2) Try It – Find the Resultant Vector ◼ ◼ Ex Sketch the arrow for each vector sum ◼ Ex Find the vector sum in each case ◼ Ex Describe the missing vector v if adding it to the given vector produces the resultant shown. a) w = (− 2, − 3) resultnt = (3, − 4 ) b) s = (− 2, − 3) resultnt = (− 5, 0) ◼ Ex Sketch the difference vector u −v s−r ◼ Ex Find the vector difference in each case u −v s−r ◼ Ex Describe the missing vector v if subtracting it from the given vector produces the resultant shown. a) w = (− 2, − 3) resultnt = (3, − 4 ) b) s = (− 2, − 3) resultnt = (− 5, 0) ◼ Ex Two people are pulling on an object. The applied forces are 200N & 400N, but in directions 30o & 135o. The same effect could be produced by a single force. What is the strength of this force? ◼ Ex A plane is flying northeast at a speed of 500km/h when it encounters an easterly wind blowing at 60km/h. What is the plane’s speed if this speed equals the vector sum of these two speeds? Properties of Addition and Subtraction ◼