Physics 9/19/2011 Vectors

1. Warmup: An airplane is flying north at 75 m/s. A tailwind of 25m/s kicks up (a tailwind is coming from behind the plane). How fast is the plane flying relative to the ground? With the same wind, how fast would the plane be traveling relative to the ground if he turned around and flew the opposite direction? Physics 9/19/2011Vectors

2. Notes for your notebook—words you’ll need to know • Magnitude • Sine • Cosine • Tangent • Right triangle • Pythagorean Theorem • Hypotenuse • Vector • Scalar • Resultant • Projectile motion • Circular motion • Centripetal acceleration • Frame of reference

3. OOOOh, Vectors are scary • No, they aren’t. In fact, you already know what a vector is. • Vector is a quantity with: • Magnitude • Direction Examples of vector quantities: displacement, velocity, acceleration, force, momentum

4. Wait, isn’t that pretty much everything? • NO! • For some quantities, there is no direction. • Speed and distance are two we have already discussed • What are some others you can think of? Tell your neighbor • Some examples: time, work, energy • These quantities can be added and subtracted with a regular old four function calculator

5. Back to vector quantities • For our airplane, we found the resultant velocity by simply adding or subtracting. • This ONLY WORKS when vectors are PARALLEL • What happens when vectors are not parallel? • When you add scalar quantities (numbers) you get a “sum” • When you add vectors, you get a resultant

6. Representing vectors • Your book uses boldface to represent a vector, eg: v=25 m/s • I will draw a little hat on top of it. • We show magnitude and direction by drawing arrows to represent vectors • Direction is represented by an angle • Magnitude is represented by the length of the arrow

7. Adding Vectors graphically Tip to tail method- • Put the “tip” of the first vector on the “tail” of the second vector • If you draw vectors to scale and perfectly, then you can use a protractor and ruler to measure the resultant vector http://www.walter-fendt.de/ph14e/resultant.htm

8. Practice vector equations

9. Practice tip to tail

10. Can you draw perfectly? • Maybe • For those of us who cannot, veehaf udder vays • Namely, we “resolve” the vector into its “components,” add the components, then turn it BACK into a vector using the Pythagorean theorem.

11. Right Triangles—a review

12. Pythagorean Theorem A2+B2=C2

13. Cool website • http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm

14. Example—ON Warmup • An archaeologist climbs the Great pyramid in Giza, Egypt. If the pyramid’s height is 136m and its width is 230m, what is the magnitude and direction of the archaeologist’s displacement while climbing from the bottom of the pyramid to the top?

15. Resolving Vectors on w/up • Find the component velocities of a helicopter traveling 95 km/hr at an angle of 35° to the ground.

16. Break it down and add it up While Dexter is on a camping trip with his boy scout troop, the scout leader gives each boy a compass and a map. Dexter's map contains several sets of directions. For the two sets below, draw and label the resultant (R). Then use the Pythagorean theorem to determine the magnitude of theresultant displacement for each set of two directions.

17. Dexter walked 50 meters at a direction of 225° and then walked 20 meters at a direction of 315°.

18. Dexter walked 60 meters at a direction of 135° and then walked 20 meters at a direction of 45°.

19. In a classroom lab, a physics student walks through the hallways making several small displacements to result in a single overall displacement. The listings on the next slide show the individual displacements for students A and B. Simplify the collection of displacements into a pair of N-S and E-W displacements. Then use Pythagorean theorem to determine the overall displacement.