INTRODUCTION TO VECTORS

Vectors

Scalar quantities are expressed by magnitude only Scalar quantities are mass (example: 43.6 g),

time (example: 56 s), and distance (example: 1.4 m). Note that these quantities only state “how much” and are expressed by a number and a unit.

Vectors

Vector quantities are expressed by magnitude and direction. One example of a vector quantity is force (example: 20 N, down). What kind of force have we studied which always acts in a downward direction?

WEIGHT

Vectors

When we describe motion of an object, sometimes direction is important and sometimes it is not. For example:

We use distance to describe the change in position of an object without any particular direction. This means that distance is a scalar quantity.

VECTORS

If Jackson East walks 5 blocks to school, then 5 blocks home to get

his homework which he forgot, then 5 blocks back to school, he

has walked a total distance of ________________ blocks.

Vectors

When the direction is important, we use displacement. This is the change

in position in a certain direction. Displacement is a vector quantity. In the example above, if the school is east of his house, what is Jacksons’

displacement?

Vectors

Speed and velocity are also different.

Velocity is speed in a certain direction.

This means that velocity must be a vector,

and speed must be a scalar quantity.

55 mi/h is an example of scalar.

25 m/s, south is an example of a vector.

Vect

ors

Vectors are drawn using

an arrow-tipped line.The length of the line

represents the magnitude of the vector while the direction

of the arrow represent

the direction of the

quantity. The arrow are

very useful for solving

problems in which vectors

need to be combined.

Vectors

The diagram represents an airplane flying east at 125 km/h. There is a 25 km/h tail wind. (which means that it blows in the same direction as the plane.)

VectorsAlways start with a bold dot. The long

vector represents the velocity of the plane. The short vector represents the velocity of the wind. Start at the dot and draw the

first vector. Then place the tail of the next vector on the head of the last one. The

resultant (one vector have the same effect as combined vectors) is always drawn from the starting dot to the last arrow head. This is called the head to tail method for solving

vector problems.

Vectors

What is the resultant of a plane flying 125 km/h due east with a tail wind blowing due east at 25 km/h? Draw a picture and solve

the problem.

VECTORS

What is the resultant velocity if you are driving 40 km/h due north in a sever thunderstorm if the wind is blowing due north at 3 km/h?

VECTORS

What if the vectors are in opposite directions? Es muy facil!!! We’ll still draw our vectors “head to tail” and find the resultant. Here’s an example:

A hiker walks 56 km due west, then turns around and walks 25 km due east. What is the hiker’s displacement? (Remember, draw the

resultant from the starting dot to the head of the last vector.)