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Kinematics in 2 Dimensions Vectors Vectors and Scalars • Vector quantities are those that have both direction and magnitude…velocity, acceleration, force, displacement, etc… • Scalar quantities are those that have only magnitude…speed, distance…etc… What is a vector?... • A vector is represented as an arrow. • Multiple vectors should be pointed in the relative direction that the real vector points and be proportional to the scale of size consistent with other vectors present. • A vector can be moved anywhere in a model as long as it maintains direction and magnitude. Vector Operations • Vectors can be added by placing them head to tail until all are drawn…the resultant is a final vector drawn from the original beginning point to the final vector arrow-tip. • To subtract vectors reverse its direction 180o and draw it …finish as before. • To multiply a vector by a number, 2 for instance, double its size… to divide, change the magnitude, but maintain direction. Vector Operations….(cont’d) • When vectors are drawn to scale, you can use a ruler to measure the resultant and a protractor to measure the angles. This is called graphical resolution. • When you have values in a model, but do not use a ruler, you can use math to solve for a resultant…when the vectors are at right angles, you can use the Pythagorean theorem. Components of Vectors • When vector addition cannot be used or is not accurate enough, resolve each vector into its x and y components and add the xs and ys at the end…construct a single x and single y vector that represent the problem and draw your resultant. You can use the Pythagorean theorem since the vectors are at a right angle. Homework • Page 70 problems 1-5, 8,9,17