Scalars vs. Vectors.

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Presentation transcript:

Scalars vs. Vectors

Scalar quantities have only a magnitude (amount) Scalar quantities have only a magnitude (amount). Vector quantities have a magnitude and a direction. We represent them as arrows. Distance (d): the separation between two points. Is distance a scalar or a vector? _____________ Displacement (Δd): A measure of the change in position. Δd = final position – initial position. The sign of the value for indicates the direction. Is displacement a scalar or a vector? ______________

a) what is the distance of Car A from Car B a) what is the distance of Car A from Car B? ___________ b) what is the distance of Car B from Car A? ___________ c) what is the position of Car A? ____________ of Car B? ____________ d) what is the displacement of Car A measured from Car B? ____________ e) what is the displacement of Car B measured from Car A? ____________

When adding vectors we use vector addition or the tip-to-tail method. Ex: A student walks 5 m east and then 3 m west. What is the distance (scalar) travelled? What is the student’s displacement (vector)? d = 5 m + 3 m = 8 m Draw the vector arrows: 5 m east 2 m east 3 m west Resultant or “net” vector When adding vectors we use vector addition or the tip-to-tail method.

Ex: A polar bear meanders 275 m east and then turns around and ambles 425 m west. What was the distance travelled by the bear? b) What was the bear’s displacement?

Ex: A little girl takes her dog for a walk around a city block as shown. What is the distance travelled? What is her final displacement? What was her displacement at B? What was her displacement at C? 115 m 125 m Start/ Finish A B C N

Ok this can get a little confusing… Describe the following angles… 1 θ 2 θ 3 θ 4 5 6 θ θ θ

Add the following vectors and find their resultant magnitudes and directions. 15 m East and 25 m North 220 m North and 80 m West 2.2 m South and 1.8 m North 150 m East and 180 m South 45 m South and 30 m East and 15 m North Remember to add tip-to-tail! When adding vectors does it matter which one you add first?