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