Vectors Physics Book Sections

Two Types of Quantities SCALAR Number with Units (MAGNITUDE or size) Quantities such as time, mass, temperature. Ex: They traveled 30 miles. (Distance) VECTOR Number with Units (MAGNITUDE or size) Plus DIRECTION! Quantities such as velocity, acceleration, force. Ex: They traveled 30 miles due east. (Displacement)

INTRODUCING “VECTOR”

NOTATION

Adding Vectors – Same Direction

Adding Vectors – Opposite Direction

Adding Vectors Mathematically

Adding Vectors Graphically When we add vectors together, the result is called a resultant vector. There are 2 methods for drawing resultant vectors in diagrams. Tip to Tail Method – AKA Triangle Method Parallelogram Method You may use whichever method makes more sense to you!

Adding Vectors – Tip to Tail Method 1. Draw one vector 2. Draw the second vector, beginning at the end of the first. 3. Draw the resultant vector stretching from the beginning of the first to the end of the second vector.

Adding Vectors – Parallelogram Method 1. Draw both vectors with a common starting point. 2. Make a parallelogram by drawing 2 more sides. 3. Draw the resultant vector stretching from the starting point to the farthest corner of the parallelogram.

Adding Perpendicular Vectors When two vectors are perpendicular to each other, the resultant vector will be the hypotenuse of a right triangle. We will use the Pythagorean Theorem and Trigonometry to find the magnitude and direction of the resultant vector.

Adding Perpendicular Vectors

Vector Components Sometime we know a vector and it can help to break it into it’s vertical (y) and horizontal (x) components. Ex: You know how far northwest someone traveled, but you want to know how far north and how far west. We can resolve the vector into its components using trigonometry.

Vector Components

Vector Components Shortcut To find the vertical and horizontal components of a vector, you will always multiply the hypotenuse by the sine and cosine of the angle. USUALLY the angles in our diagrams are measures from the x axis If this is the case, then sin will find the y component and cos will find the x component.

Vector Components

Problem Solving #1

Problem Solving #2

Problem Solving #3

Problem Solving #4