1. Vectors Part 2 Projectile Motion Vectors Part 2 PVHS Physics

2. Essential Questions  What is a vector?  What is the difference between a scalar and a vector?  How do you add and subtract vectors?  What are the horizontal and vertical components of a vector?  What is projectile motion?  How can the motion of a projectile be described by its horizontal and vertical vector components?

3. What we know…  A scalar has magnitude but no direction  A vector has magnitude and direction  The resultant is a vector representing the sum of two or more vectors  Vectors can be added graphically using the triangle or the parallelogram methods

4. Try this…  An A-10 normally flying at 80 km/hr encounters wind at a right angle to its forward motion (a crosswind). Will the plane be flying faster or slower than 80 km/hr?

5. 60 km/hr Crosswind 80 km/hr Is the resultant greater than or less than 80 km/hr? 80 km/hr 60 km/hr Add the vectors Resultant

6. Vectors © 1996-2009 The Physics Classroom, All rights reserved.

7. 60 km/hr Crosswind 80 km/hr Is the resultant greater than or less than 80 km/hr? 80 km/hr 60 km/hr Add the vectors Resultant What we know…

8. 2-D Coordinate System  In 2-D, a good reference is the x-y coordinate plane X Y Remember… we can move a vector as long as we don’t change magnitude or direction

9. 2-D Coordinate System X Y  Once you establish a coordinate system or frame of reference, you can begin to analyze vectors mathematically  First, resolve the vector into its x-component and its y-component

10. Determining Magnitude  The component vectors can represent the change in x and the change in y for the vector  To find the magnitude, d, of the vector, we use the Pythagorean Theorem: X Y xx yy d

11. Determining Direction  Once we have a frame of reference, the vector will make an angle, with the x-axis  We can use the tangent function to determine the value of  X Y xx yy d  If using a calculator, be sure to set degrees or radians as appropriate

12. Try this…  While following directions on a map, a pirate walks 45.0m north then 7.5m east. What single distance and direction could he have walked to reach the treasure?

13. X Y 45.0m 7.5m d 

14. Component Vectors  Just as we can add two vectors to create a resultant… 80 km/hr 60 km/hr Resultant

15. Component Vectors  Any vector can be broken down into two vectors that are at right angles to one another These vectors are called “component vectors” The process of determining the components is called “Resolution” Velocity Vertical Component Horizontal Component

16. Resolving Components  If we know the magnitude, d, and direction,  we can also find the x and y components X Y xx yy d 

17. Try this…  How fast must a truck travel to stay directly beneath and airplane that is moving 105 km/hr at an angle of 25 degrees to the ground? X Y V=105 kph   V truck =?

18. Adding Vectors  Algebraically

19. Demo  Vector A=4.5m/s @ 35 degrees  Vector B=6.5m/s @ -40 degrees  Find A+B

20. Try this…  A ranger leaves his base camp for a ranger tower. He drives 35 o south of east for 25.5 km and then drives 65 o north of east for 41.0 km. What is the displacement from the base camp to the tower?

21. What we know…  What is a vector?  What is the difference between a scalar and a vector?  How do you add and subtract vectors?  What are the horizontal and vertical components of a vector? http://www.physicsclassroom.com/Class/1DKin/U1L1c.html

22. Questions?