Vectors and Scalars

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

Vectors A vector quantity is a quantity that has both magnitude and a direction in space Examples of Vector Quantities: Displacement Velocity Acceleration Force

Vector Diagrams 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

Resultant of Two Vectors The resultant is the sum or the combined effect of two vector quantities Vectors in the same direction: 6 N 4 N = 10 N 6 m = 10 m 4 m 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 Vectors in opposite directions: 6 m s-1 10 m s-1 = 4 m s-1 6 N 10 N = 4 N

Practice with vectors 10m due North + 7m due South Draw a vector diagram: Determine if you should add or subtract the vector quantities: Do the math and record your vector answer: be sure to include a direction

#2 15km due East + 20km due West + 55km due East

From a word problem… 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 is 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 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 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 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?

What if they are perpendicular to each other? 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? 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

A duck flies south at 35 km/hr A duck flies south at 35 km/hr. It encounters a west moving wind at 6 km/hr. What is the resultant?

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?

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