Ch. 3, 2-D Motion and Vectors

1. Ch. 3, 2-D Motion and Vectors

2. *A Scalar is a quantity with a magnitude but no direction. Like volume or page numbers. • *A Vector is a quantity with a magnitude and direction. Like velocity or acceleration.

4. Put vectors in boldface, like v for velocity. • *The answer from adding two vectors is called the Resultant.

5. Adding vectors

6. You can move vectors around, as long as they point at the same angle when moved. • Exp, a car moving.

7. You can add vectors in any order. • To subtract a vector, add its opposite.

8. *Multiplying a vector by a scalar changes the vector’s magnitude. • *Multiplying by a negative flips the vector to travel in the opposite direction.

9. Properties of Right Triangles • *Pythagorean Theorem: c2 = a2 + b2 • *Soh cah toa • *Total of angles in ANY triangle = 180⁰

10. Use Soh Cah Toa to find the angle of a resultant vector. • Exp: 10 in x, 12 in y • Use Pythagorean to find the magnitude of the resultant.

11. Resolving Vectors into X and Y components. Use Soh Cah Toa. 33 degrees. V = 8

12. Adding two Vectors that are NOT perpendicular to each other • Break the two vectors into their x and y components. Then use these to create a right triangle. • Show a picture on board

13. A camper walks 4.5 km at 45 degrees north of east. Then she walks 4.5 km due south. Find the angle and displacement of the resultant. • Answer: 3.4 km, 22 degrees south of east.

14. A plane flies 118 km at 15 degrees south of east, and then flies 118 km at 35 degrees west of north. Find the magnitude and displacement. Answer 81 km, 55 degrees north of east

15. Projectile Motion • Resolve vectors into x and y components, then use kinematic equations (from table 4). • Draw Picture

16. *Objects that are thrown or launched into the air are called projectiles.

17. I wish I was Brett Favre!

18. Projectiles follow parabolic trajectories.

20. Projectile motion is free fall with an initial horizontal velocity and an initial vertical vel. • The horizontal component in velocity in projectile motion is considered to be constant. So, initial velocity (x direction) = final velocity (x direction).

21. Delta X = Vxdeltat

22. *Max height of projectile: Solve for y direction displacement when final velocity in Y direction is 0.

23. *Hang Time: Solve for time when final velocity in Y direction is 0; then multiply by 2.

24. A bridge is 321 m high. You kick a rock horizontally off the bridge. The magnitude of the rock’s horizontal displacement is 45 m. Find the speed at which the rock was kicked: • 5.6 m/s

25. Break vectors into components in order to analyze objects thrown at an angle.

26. A Zookeeper finds a monkey hanging from a 5 m high lightpole. She fires a dart from a height of 1 m above the ground. She is 10 m from the pole when she fires. She fires the dart at 50 m/s. At the moment she fires, the monkey drops a banana. Will the dart hit the monkey, the banana, or both? • 4.77 m above the ground, banana.

27. Pg. 110, # 34 • A shell is fired from the ground with an initial speed of 1,700 m/s at an angle of 55 degrees. What is the horizontal range and the time in the air? • 2.77E5 m, 284 s

28. Velocity Measurements differ in different frames of reference. • See pg. 102 Figure 19.

29. An ostrich runs to the East at 5 m/s. It is chasing a truck, which is driving to the East at 20 m/s. What is the velocity of the truck from the bird’s perspective?

30. An ostrich runs to the East at 5 m/s. It is chasing a truck, which is driving to the East at 20 m/s. What is the velocity of the bird from the semi’s perspective?

31. An ostrich runs to the East at 5 m/s. It is chasing a truck, which is driving to the East at 20 m/s. What is the velocity of the bird from a bystander’s perspective?

32. Optimus Prime drives to the East at 15 m/s. A minivan drives to the West at 10 m/s. What is the velocity of Optimus according to the van?

33. Vector Problem • You are the captain of a pirate ship. You need to travel 500 meters to the east to get to the Prime Meridian. You sail 10 m/s due east. There is a current at 1 m/s due north. How far do you actually travel to get to the Prime M.?

34. Practice Problems for Test • 1. You launch a basketball horizontally off a cliff. The ball travels 50 meters horizontally. The cliff is 120 m high. What velocity did you launch the ball with? • 2. You launch a football at 24 degrees with a velocity of 30 m/s. What is the range, the hang time, and the maximum height? • 3. A plane travels 30 degrees north of east for 400 km, then it turns around and travels 34 degrees west of south for 500 km. What is the direction and magnitude of its total displacement?

35. Projectile Tennis Lab on the tennis courts • Hit from close to the ground. • 1. Hit the ball. Measure the hang time and displacement. Solve for Vi and the angle of launch. • 2. Repeat for a different type of hit. • 3. Predict a Vi and an angle of launch that would enable a perfect hit from baseline to baseline (23.77 m). Now try it! • (Alternatively, you can throw a ball and have someone catch it at about the same height that it was launched from.)

36. Review:

37. Do a horizontal and angled launch problem.

40. If you are running at 5 m/s in a 2 m/s headwind, how long will it take you to run 3,000 meters?

41. How do you find the resultant of two vectors that are perpendicular?

42. How do you find the resultant of two vectors that are not perpendicular?

43. What is the difference between a scalar and a vector?

44. What is meant by x component and y component of a vector? How are they found?

45. Magnitude vs. direction.

47. Partner Review

48. Explain how horizontal and vertical velocity are different in projectile motion:

49. A bird flies 15 degrees west of north for 23 km. Then it turns and flies 20 degrees east of north for 34 km. What is the bird’s total displacement and angle of displacement?

50. There are two baseballs that start 2 meters above the ground. Both balls are released at the same time. One is thrown horizontally at 20 m/s and the other is simply dropped. Which one will hit the ground first?