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Vector Components • 2-D Coordinate Systems • Vector Components • 2-D Vector Algebra Outline Coordinate Systems • We have been using Cartesian Coordinates • In 2-D, this has x and y axes • The positive y-axis is located 90 counter-clockwise from the positive x-axis • The fact that the axes are 90 to each other allows us to have x and y components which are independent Draw a set of Component Vectors How to find Component Vectors y A Ax A cos( ) Ay A sin( ) x SOH CAH TOA Just remember: SOH CAH TOA y Ay A cos( ) Ax A sin( ) A x You can always use sin() instead of cos () use 90 - Ratios you should know QQ29: 2-D Components Exercise Determine the numerical values of the x and y components of each vector: y 120 y A 5 x x 45 10 B Ax = __________ Ay = __________ Bx = __________ By = __________ Don’t use a calculator. Given Ax and Ay , you can find the magnitude and Magnitudes direction of A : y A Ax Ay A Ax Ay 2 2 tan1 (opposite/ adjacent) x QQ30: Magnitudes Example: For a particle moving with vx = 5 m/s and vy = -2 m/s. A) Draw the velocity vector on an set of x-y coordinates. B) Find v Component Notation Component notation A velocity vector v has components vx , vy y v v vx iˆ v y ˆj vy “Unit vectors” i, j: iˆ ˆj 1 vx In 3-D space: kˆ and vz . x QQ30: Magnitudes Example: For a particle moving with vx = 5 m/s and vy = -2 m/s. Express v using unit vectors. Ex. Unit Vectors Worked Example: Unit Vectors Two students are moving a refrigerator. One pushes with a force of 300 N along the horizontal, the other lifts with a force of 400 N along the vertical. What is the resultant force when expressed using unit vectors? C=A+B What if the vectors are not directed along an axis? AB C (Ax iˆ Ay ˆj) (Bx iˆ By ˆj) (Cx iˆ Cy ˆj) C x Ax Bx C y Ay By C By B A Ax Ay Bx Example: A=2i+3j and B=-5i-7j What is A+B and A-B ? Do for next class: Read: Sections 4.1, 4.2, 4.3 Suggested problems: 4.2, 4.3, 4.4