1. Regents Physics  AGENDA Start Chapter 4: Vectors Graphical vector addition / subtraction HW:

2. Drawing Vectors  A vector has magnitude and direction each vector is drawn to scale and includes a tip, indicating a direction Tail Tip N S W E The coordinate axis system defines the direction of the vector The length is defined by creating a scale Scale 1.0 cm = 10.0 m/s V = 100.0 m/s east

3. Tip to Tail Triangle Method..How do we graphically add/subtract vectors V1V1 V2V2 Resultant Vector (R) = V 1 + V 2 The resultant vector is an equal expression of vectors V 1, V 2 Tail of V 2 to tip of V 1

4. Tip to Tail... V 1 east V 2 north Put on axis and use tip to tail method N S WE V 1 east V 2 north R Measure the length of the resultant!

5. Vector addition example  A person walks 24.0 m north and 12.0 m east. Determine the position and magnitude of the resultant vector of this motion. First, make a scale for the vectors Draw a coordinate axis Draw and the label the vectors Draw and measure the resultant vector!

6. Vector addition problem #2  A plane flies at 200.0 miles per hour north when it encounters a crosswind of 80.0 miles per hour from the west. Determine the position and magnitude of the resultant vector of this motion.

7. These are equal expressions…right?!

8. This method can also be used when we are not using tip to tail addition… and we also get the same results! Notice both vectors start at the same origin

9. Example  Find the resultant vector of the following two vectors We use dashed lines to represent the mirror images of the vectors

10. Rotate green A vector 180 degrees and give it a negative sign! Just remember..tip to tail Our resultant vector is now B - A and has a different magnitude and direction! A B

11. A car drives 100.0 km at an angle of 35 degrees north of east. Find the vectors d 1 east and d 2 north of this motion. 35 ° V 2 north V 1 east Just draw and measure the vectors! What if we START with the resultant?

12. Practice Problem...  A package is dropped from a plane and is “off target” by 100ft to the west. If the distance to the ground is 500ft. (a) What is the resultant vector of this motion? (b) What is the angle from the negative y - axis of the resultant vector?