Objectives The student should be able to: 1.Distinguish between a scalar and a vector 2.Combine vectors using graphical methods 3.Sketch a vector diagram, and trigonometrically solve for the components 4.Sketch the components of a vector, and trigonometrically solve for the resultant

Scalars Need to Know Specified by a magnitude and a unit –4 m/s –10 kg –10 x m

Vector Need to Know Specified by a magnitude and unit AND DIRECTION –4 m/s heading west –10 x m north –10 m/s 2 down As long as the direction and magnitude are kept the same you can move the vector anywhere

Vector Representation Need to Know On a drawing, a vector is represented by an arrow The length of the vector is proportional to the magnitude In print, a vector is usually bold In hand written work, a vector can be indicated by an arrow over it

Vector Addition Need to Know If they are collinear, simple arithmetic can be used Simple arithmetic can not be used if they are not collinear The sum of a given set of vectors is called the resultant

Example Suppose you drive 200 km to the east and then 50 km to the west. What is your total distance traveled? 200 km east (+) 50 km west (-) Since they are parallel I can add arithmetically I assume everything going to the right is positive And everything going to the left is negative Total distance traveled = 200 km – 50 km = 150 km to east (+) 150 km east (+)

What if they are not collinear or parallel? We can add them together graphically –Tip to tail method –Parallelogram method We can add them together mathematically with trigonometry (oh my!)

Graphical Addition Need to Know Tip to Tail method: –Draw first vector to scale –Draw second vector to scale, placing its tail at the first vector’s tip (make sure your directions are correct!) –Draw an arrow from the tail of the first vector to the tip of the second vector. This is the resultant of the two vectors –Approximate the length of the resultant

Tip to Tail Method 20 m 15 m Approximately ≈ m + 15 m Tails Line up Tips Line up Tip to tail

Tip to Tail Method + 20 m 10 m ≈ 25

Website Example Adding vectors tip to tail Tip to tail with numbers

+ = 10 Resultant

+ =

Practice Do Problems on p 109 of your textbook Answers: 21a o 21b. 13 blocks yd o, o m, m km east, 1.31 km north o

Graphical Addition Need to Know Parallelogram method –The tails of the vectors are drawn from a common origin –Parallelogram is constructed using these two vectors as adjacent sides –The resultant is drawn from the common origin –We can only add two at a time with this method

Parallelogram Method + 20 m 15 m Tails are together 20 m 15 m Create parallelogram with opposite sides ≈ 23 m

Parallelogram Method ≈

+ =

+ =

Graphical Addition Bottom Line: Gives a good approximate direction and magnitude of the resultant vector. For the most accurate results you must add your vectors mathematically!! That is next ….. but first what do you recall about vectors

94 m/s is a 1.Vector 2.Scalar 3.Direction Correct answer is 2—scalar

94 m/s going west is a 1.Vector 2.Scalar 3.Direction Correct answer is 1--vector

A vector has 1.Direction and magnitude 2.Magnitude only 3.Direction only Correct Answer is 1

The drawing indicates what type of vector addition? 1.Tip to tail 2.Parallelogram Correct Answer is 2

The drawing indicates what type of vector addition? 1.Tip to tail 2.Parallelogram Correct Answer is 1

Practice Quest VectorsDue 12/15-16