1. Physics I Unit 4 VECTORS & Motion in TWO Dimensions http://hyperphysics.phy- astr.gsu.edu/hbase/vect.html#vec1 Web Sites

2. Objectives: Calculate and / or measure Velocities Vectors using graphical means Calculate and / or measure Velocities Vectors using algebraic means Do Now  Page 117 #1 Homework Unit 4 Lesson 1 IN CLASS: Page 121 Example 1  Pg 121 – 125 Practice Problems: 1-9 ODD:  Pg 141 – 142 Problems: 80 – 89 all  80 – 88 EVEN 

3. Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature

4. Addition of Vectors – Graphical Methods For vectors in one dimension, simple addition and subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates. 8 km + 6 km = 14 km East 8 km - 6 km = 2 km East

5. Addition of Vectors – Graphical Methods Even if the vectors are not at right angles, they can be added graphically by using the “ Head to Tail ” method: 1. Draw V1 & V2 to scale. 2. Place tail of V2 at tip of V1 3. Draw arrow from tail of V1 to tip of V2 This arrow is the resultant V (measure length and the angle it makes with the x-axis) Same for any number of vectors involved.

6. Addition of Vectors – Graphical Methods The parallelogram method may also be used; 1. Draw V1 & V2 to scale from common origin. 2. Construct parallelogram using V1 & V2 as 2 of the 4 sides. Resultant V = diagonal of parallelogram from common origin (measure length and the angle it makes with the x-axis)

7. Addition of Vectors – Graphical Methods If the motion is in two dimensions, the situation is somewhat more complicated. Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.

8. Adding Vectors by Components Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other. Unit 4 Lesson 2

9. Adding Vectors by Components If the components are perpendicular, they can be found using trigonometric functions.

10. Objectives: Word Problems with VECTORS Do Now Page 117 #2 Page 121 #4 Homework Pg 141 – 142 Problems: 80 – 89 all Unit 4 Lesson 2 IN CLASS: Pg 125 Section Review Problems: 11 -15 ALL http://hyperphysics.phy- astr.gsu.edu/hbase/vect.html#vec1

11. Objectives: -Determine Equilibrium Forces -Determine the motion of an object on an inclined plane with and without friction Do Now  Page 128 #17  Next SLIDE(s) Homework  Page 133 Practice Problems: 33- 41 odd Unit 4 Lesson 3 IN CLASS: Pg 133 Example 5 Pg 134 Example 6

12. DO NOW 3 Vector Problem Graphically Unit 4 Lesson 3

13. Solving the components X Components Ax = 44.0 * COS (28.0) = 38.85 Bx = 26.5 *COS (124) = - 14.82 Cx = 31.0 * COS (270.0) = 0.00 X total = 24.031 Y Components Ay = 44.0 * SIN(28.0) = 20.56 By = 26.5 *SIN(124) = 21.97 Cy = 31.0 * SIN(270) = - 31.0 Y total = 11.53 V = √{[24.031] 2 + [11.53] 2 } V = √{[710.418]} = 26.65367 m/s = 26.7 m/s 3 Vector Problem Θ = Tan -1 {11.53/24.031} Θ = Tan -1 {0.4797969} Θ = 25.6315 degrees Θ = 25.6 degrees Unit 4 Lesson 3

14. Objectives Do Now Homework Unit 4 Lesson # IN CLASS:

15. Objectives Do Now Homework Unit 4 Lesson # IN CLASS:

16. Objectives Do Now Homework Unit 4 Lesson # IN CLASS:

17. Objectives Do Now Homework Unit 4 Lesson # IN CLASS: