1. Notes: Vectors

2. Scalars Scalars—quantities with only magnitude (size) EXAMPLES:Run 2 km—distance Travel at 40km/h—speed Eat 1 c of kale—volume Talk for 30 min—time Distance, speed, volume, and time are all scalar quantities. To add or subtract them, use arithmetic.

3. Vectors Vectors—quantities with both magnitude and direction Examples:Travel 20 km due east---displacement Drive 100 km/h due North---velocity Accelerate 9.8m/s 2 downward--acceleration Displacement, velocity, and acceleration are vectors. To represent vectors, use arrows. To add and subtract vectors, use geometry.

4. Represent vectors with arrows, the length of the arrow corresponds to the magnitude of the vector and the direction of the arrow shows the direction of the vector. The dotted end of the vector is called the tail and the arrow end is called the head. 10 km/h due E Drawing Vectors

5. For objects that only travel along a line… You can use + and – to designate direction. For instance, if N is the positive direction, then ___ is the negative direction. If up is the positive direction, then _____ is the negative direction. If right is the positive direction, then ____ is the negative direction.

6. VectorMagnitudeDirection What about vectors that point in other directions?

7. Rules for Adding Vectors When you add vectors, you must account for their direction. In vector math, 2 + 2 can equal anything from 0 to 4 depending on the directions of the two vectors!

8. To add vectors 1. Draw the first vector you want to add. 2. Draw the second vector you want to add. Place its tail next to the head of the first vector. 3. Draw the answer head-to-head and tail- to-tail. Your answer is called the resultant or resultant vector.

9. Example 1 A dog runs 30 km due W, then turns and runs due E 18 km. a. Find his displacement. b. Find the distance he traveled.

10. Example 2 A chicken flies due N at 2m/s while the wind blows it due N at 0.5 m/s. Find her resultant velocity.

11. Example 3 A swimmer crosses a river heading due E at 0.3 m/s. The river’s current flows due S at 0.1 m/s. Find the swimmer’s resultant velocity.

12. Definition Projectile—an object moving through space affected only by gravity and, if present, air resistance

13. Just like a river problem… The horizontal and vertical components of a projectile’s motion are independent of each other—changing one does not affect the other. To find:Look at: time in airVertical distancehorizontal

14. Example: The motion in the horizontal direction is independent of motion in the vertical direction!

15. How to solve projectile problems To find:Look at:Why?Equations: Time in airVertical motionIn the vertical direction, projectiles accelerate downward at 9.8 m/s 2 because of gravity. rangeHorizontal motion In the horizontal direction, projectiles travel at a constant velocity because there are no forces acting on them.

16. Components of Motion In the horizontal direction, projectiles travel at a constant velocity. –WHY? There is no force to change the velocity in this direction. In the vertical direction, projectiles accelerate downward at 9.8 m/s 2. WHY? Gravity pulls the object downward.

17. EXAMPLE 1 A ball is thrown at 4 m/s from a cliff that is 20 m high. a)How long does it take to reach the ground? b)How far away from the base of the cliff does it land?

18. Example 2 A cannonball is shot upward at 30 m/s at an angle of 60 o with the ground. a.Find the horizontal and vertical components of the cannonball’s initial velocity. b.Find the time it takes the cannonball to reach the top of its path. c.Find the cannonball’s total time in the air. d.Find the horizontal distance the cannonball travels.

19. Quiz Review 1 A kangaroo hops 12 m due N, then15 m due E. Find: a) the distance traveled; b) the displacement.

20. Quiz Review 2 A condor flies due S at 2 m/s while the wind blows him due N at 0.5 m/s. Find his resultant velocity—both magnitude and direction.

21. Quiz Review 3 A fish swims due W directly across a 50-m wide river at 2 m/s. The current flows due S at 1 m/s. Find: a) the time for the fish to cross the river. b) how far downstream the fish is when he gets to the other side. c) the fish’s resultant velocity—both magnitude and direction.