Vectors and Scalars

A scalar quantity is a quantity that has magnitude only and has no direction in space

Examples of Scalar Quantities:

Length Area Volume Time Mass

A vector quantity is a quantity that has both magnitude and a direction in space

Examples of Vector Quantities:

Displacement Velocity Acceleration Force

Vectors are arrows that show the magnitude and direction of a vector quantity

The length of the arrow represents its magnitude

The direction of the arrow shows its direction

Vectors in opposite directions:

6 m s-1 10 m s-1 = 4 m s-1

6 N 10 N = 4 N

Vectors in the same direction:

6 N 4 N = 10 N

6 m= 10 m

4 m

The resultant is the sum or the combined effect of two vector quantities

If two vectors are in the same direction, add them together and keep that direction

If two vectors are in the opposite direction, subtract them and keep the direction of the larger

vector

10m due North + 7m due South1. Draw a vector diagram:

2. Determine if you should add or subtract the vector quantities:

3. Do the math and record your vector answer: be sure to include a direction

15km due East + 20km due West + 55km due East

An airplane flies at 200 km/hr East into a headwind of 25 km/hr. What is the resultant vector?**a headwind is a wind that pushes against the head or the front of the plane so it going in the same or opposite direction of the plane?

67 cm due East + 30cm due West

Ann is at the airport and is in a rush. She normally travels north at 2 m/s. If she gets on a “moving sidewalk “ that travels at 2 m/s north and walks on it, what will be her resultant velocity?

An action hero is running on top of a train traveling at 55m/s. If our hero is moving toward the front of the train at a speed of 5 m/s, what is our hero’s resultant velocity?

You are on a bus traveling 47 m/s forward. You go to the back of the bus to visit your friend you are walking at a speed of 3 m/s. What is your resultant velocity?

First, draw the vectors so they are “tail” to “tail” to each other

Draw two dashed lines to create a parallelogram with vectors as the other two sides

The resultant is found by drawing the diagonal that connects the corner formed by the vectors and the opposite corner formed by the dashed lines This is known as the parallelogram law It results in a right triangle and you find the magnitude of

the resultant by using the Pythagorean theorem A2 + B2 = C2

Where A and B are the two vectors and C is the resultant

Ex: An airplane is flying at a speed of 80 km/hr North, but there is a strong wind blowing at 60 km/hr to the east. What is the resultant vector for the plane?

35cm due North + 85cm due East

A NYC tourist walks 5 blocks East across town and 7 blocks North up town. What is the resultant vector?

A rock is thrown vertically at 6 m/s from a train moving horizontally at 4 m/s. What is the resultant vector?

What is a scalar quantity? Give 2 examples What is a vector quantity? Give 2 examples How are vectors represented? What is the combination of 2 vector

quantities? What is the parallelogram law?