VectorsVectors

What is a vector quantity?

Vectors Vectors are quantities that possess magnitude and direction. »Force »Velocity »Acceleration

What are scalar quantities?

Scalars Scalars are quantities that possess only magnitude. How much money you have How old you are How tall you are Temperature Pounds Speed Length

Represent the following vectors A wind velocity of 20 mph due north A boat traveling 4 knots per hour heading east A car traveling 60 mph heading south

Equal Vectors Same length Same direction

Parallel Vectors

Adding Vectors

Three Methods for Adding Vectors Tail to Head Method Parallelogram Method Component Method

Tail to Head Method

Adding Vectors Tail to Head Draw Vector A with the correct length and angle. Draw Vector B with the correct length and angle, but such the Vector B’s tail starts at the head of vector A. The Vector C is then represented by an arrow from the tail of Vector A to the head of Vector B.

Adding Vectors Same direction

Adding Vectors Opposite directions

Adding Vectors Components

Parallelogram Method

Vector 1 Vector 2 Resultant Vector

Component Method

Find the sum of Vector 1 and Vector 2. Vector 1 is 25 m 50  N of E Vector 2 is 10 m 45  N of W

Component Method Using Trigonometry, find the x-component and the y-component for each vector. Add up the x-components. Add up the y-components. Use the Pythagorean Theorem and the trig functions to get the size and direction of the resultant vector.

Finding the x-component X-component Y-component  Resultant vector

Finding the x-component Vector 1 is 25 m 50  N of E X-component Y-component 50  25 meters X-component = 25 * cos 50 X- component (vector 1) = 16.1 m

Finding the y-component X-component Y-component  Resultant vector

Finding the y-component Vector 1 is 25 m 50  N of E X-component Y-component 50  25 meters y-component = 25 * sin 50 y- component (vector 1) = 19.2 m

Finding the x-component Vector 2 is 10 m 45  N of W X-component Y-component 45  10 meters X-component = 10 * cos 135 X- component (vector 2) = -7.1 m

Finding the y-component Vector 2 is 10 m 45  N of W X-component Y-component 45  10 meters y-component = 10 * sin 135 y- component (vector 2) = 7.1 m

Adding the x- components Vector 1 + Vector m m = 9 m

Adding the y-components Vector 1 + Vector m+ 7.1 m = 26.3 m

Using the Pythagorean Theorem c²= a²+ b² c²= 9²+26.3² c²= c = 27.8 meters  = 71.1  N of E

Mission Impossible

Vectors on the Go

Good Luck