Do Now: This is a diagnostic assessment. If you don’t know the answers, write down the question for full credit.  Write the direction and magnitude of.

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Presentation transcript:

Do Now: This is a diagnostic assessment. If you don’t know the answers, write down the question for full credit.  Write the direction and magnitude of the following vectors.  Break the vectors into components.  Solve for the resultant vector. =30, 78° = 14, 35°

 Do Now (10/14): *turn in Do Now’s today! 1. Solve for x:2.Find the sin, cos, and tan of the angle θ.

 Working With Vectors Day One: Breaking Vectors into Components

Review:  Vector quantities ALWAYS have a magnitude and a direction.  Vector quantities can be represented by a vector; the vector should include an arrowhead, a tail, and a label.

Drawing/Labeling Vectors  Vectors should be given a name and labeled  The name of the vector should have an arrowhead above it.  If the vector has units, they should be included in the label (N, m/s, etc.) = 20 N, 65°

Finding the Resultant Vect0r  The resultant vector is the sum of two or more vectors  We can only add vectors on the same axis; to find the resultant vector we must break all vectors in components  Vector Component: Each part of a two-dimensional vector; each component of a vector describes the vector’s influence in a specific direction (i.e. X and Y, North and East, etc.)

Vector Components

Drawing Vector Components  Draw dashed lines from the arrowhead of the vector to each respective axis  Don’t forget your labels!!!

Calculating Vector Components  x-component:  y-component:  Where B is the magnitude of the vector (i.e. if then B=48)

Example:

Practice:  Use the rest of class to solve for the components of each vector in the twelve diagrams on your paper. Please finish for homework.

Do Now (10/17):  Break the vectors into components. Be sure to draw, label and calculate the values of each vector. =30, 78° = 14, 35°

 Working With Vectors: Day 2: Solving for the Resultant Vector

Objective:  To use what we know about calculating vector components to solve for the resultant vector of two or more vectors

Sum of components  Add components on each axis:

Example:

Drawing the Resultant Vector  Draw R x and R y - these are the components of the resultant vector!!!

Drawing the Resultant Vector  To find the resultant vector, draw a vector from the origin to the point where the components of the resultant meet

Finding the Magnitude of the Resultant Vector  Magnitude is the length of the resultant vector Use the Pythagorean Theorem!

Finding the Direction of the Resultant

Do Now (10/18):  Calculate the resultant vector. Be sure to include all units, drawings, and formulas. =30N, 78° = 14N, 35°

Example #1:  How would your process for finding the resultant vector be different for this type of diagram? = 30 m, 0° =55 m, 90°

Example #2:  How would your process for finding the resultant vector be different for this type of diagram? =7 m/s, 60° = 6 m/s, 0° =10 m/s, 90°

Example #3:  How would your process for finding the resultant vector be different for this type of diagram? =7 m/s, 240° = 6 m/s, 0° =10 m/s, 90°

Practice (10/18): finish your homework first!!! Then you may do one of two things: 1. Work on your notecard 2. Work with your group on your rough draft

Graded Classwork:  Calculate the resultant vector. Be sure to include all units, drawings, and formulas. =40 m, 58° = 30 m, 0° =55 m, 90°

Do Now (10/19):  What are the steps for finding the resultant vector?  What formulas will you need to know for this quiz?  Turn in your Do Now when you’re finished!