1.2 Vectors in Two Dimensions Defining Vector Components Any vector can be resolved into endless number of components vectors. p. 11 DRDR DRDR D1D1 D2D2 D3D3 D4D4 The ability to add components vectors is key to solving all sorts of Physics problems.

1.2 Vectors in Two Dimensions p. 12 Trigonometric Rations Used in Vector Problems: CB A ѳ adjacent side opposite side hypotenuse Sin ѳ = Opposite side hypotenuse = o h Cos ѳ = adjacent side hypotenuse = a h Tan ѳ = Opposite side Adjacent side = o a Trigonometric ratios can help you solve vector problems. The rules for adding velocity vectors are the same as those for displacement and force vectors.

1.2 Vectors in Two Dimensions p. 13 Resolving Vectors into Vertical and Horizontal Components F R = 60.0 N A force of 60.0 N is applied downwards at an angle of 53 o below the horizontal. This vector can be show as the addition of two perpendicular component vectors. Vertical Component Horizontal Component Vertical Component is directed downwards into the ground: Horizontal Component is directed horizontally to the ground (may be used to move the object along the ground) Ѳ = 53 o

1.2 Vectors in Two Dimensions p. 12 Method 1: Solving by Scale Diagram F R = 60.0 N Ѳ = 53 o A scale is used (1.0 cm = 10.0 N) is drawn over the vectors. By using this scale the vertical component can be determined to be 36.0 N and the horizontal component is 48.0 N. F y = 36.0 N F x = 48.0 N Length = 4.8 cm Length = 3.6 cm

1.2 Vectors in Two Dimensions p Method 2: Resolve into Components F R = 60.0 N Ѳ = 53 o F y = cos 53 o x 60 Cos Ѳ = adj Hyp Cos 53 o = FyFy FRFR F y = 36 N F x = sin 53 o x 60 Sin Ѳ = Hyp Sin 53 o = FxFx FRFR F x = 48 N Opp By using the correct trigonometric functions both the vertical and horizontal components can be determined.

1.2 Vectors in Two Dimensions p Method 2: Resolve into Components (con’t) F R = 60.0 N Ѳ = 53 o F y = 36 N F x = 48 N To check to see if you have the right answer use Pythagorean theorem as follows: F R 2 = F x 2 + F y 2 F R 2 = F R = 60 N

1.2 Vectors in Two Dimensions More than One Vector: Using a Vector Diagram 30 o Force of gravity F g = 36.0 N String #2 String #1 Two strings support an object. To determine tension in each string a force triangle is made from the three forces. F g = 36 N Tension #2 Tension #1 30 o p. 14

1.2 Vectors in Two Dimensions More than One Vector: Using a Vector Diagram F g = 36 N F 2 = Tension #2 F 1 = Tension #1 30 o Tan 30 o = FgFg F2F2 F 2 = 36.0 Tan 30 o F 2 = 20.8 N Cos 30 o = F1F1 F 1 = 36.0 Sin 30 o F 1 = 41.6 N FgFg Each tension can be found by using the correct trigonometric function. p. 15

1.2 Vectors in Two Dimensions A Velocity Vector Problem – Vectors in Action Boats crossing rivers and Planes travelling against wind are all ideal vector problems. v r v b v p v w v r v b v R v R 2 = v r 2 + v b 2 v R = v p + v w v R = v p - v w ѳ tail wind head wind v R p

1.2 Vectors in Two Dimensions Key Questions In this section, you should understand how to solve the following key questions. Page 16 – 17 – Practice Problem #1 - 3 Page 20 – Practice Problem #1 – 3 P. 21 – Review Questions # 1 - 9