1 / 47

VECTORS AND SCALARS

VECTORS AND SCALARS. SCALARS. Vectors. Symbol for vectors:. Typed: v, a, F, x Written: . Multiplying vectors by scalars. Vector x scalar = vector. Multiplying vectors by scalars. Comparing vectors. Which vectors have the same magnitude?. Which vectors have the same direction?.

eden
Download Presentation

VECTORS AND SCALARS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. VECTORS AND SCALARS

  2. SCALARS

  3. Vectors

  4. Symbol for vectors: Typed: v, a, F, x Written:

  5. Multiplying vectors by scalars Vector x scalar = vector

  6. Multiplying vectors by scalars

  7. Comparing vectors Which vectors have the same magnitude? Which vectors have the same direction? Which arrows, if any, represent the same vector?

  8. Adding vectors

  9. Subtracting vectors (+ negative)

  10. Subtracting vectors (“fork”)

  11. Check your understanding Construct and label a diagram that shows the vector sum 2A + B. Construct and label a second diagram that shows B + 2A. Construct and label a diagram that shows the vector sum A – B/2. Construct and label a second diagram that shows B/2 - A.

  12. Adding vectors algebraically

  13. Adding vectors that are perpendicular

  14. Example A person walks 5 km east and 3 km south. What is the person’s total displacement? Hint: displacement is a vector quantity, the answer should have magnitude (km) and direction (degrees)

  15. Relative Motion • A person is sitting in a bus that is moving north 2 m/s. a)What is the passenger’s velocity relative to a person standing on the sidewalk nearby? b) What is the passenger’s velocity relative to the person sitting next to him? c) What is his speed relative to a car moving at 4 m/s in the opposite late towards the bus?

  16. Relative motion • A swimmer moves at 2 m/s in a pool. a)What will be her speed relative to a person on the river bank if she swims downstream and the current is 5 m/s? b) What will her speed be if she tries to swim against the current?

  17. A boat is crossing a river moving south with a speed of 4.0m/s relative to the current. The current moves due east at a speed of 2.0 m/s relative to the land. • How far across the river will the boat be in 2 seconds? • How far down the river the boat be in 2 seconds? • What will the boat’s total displacement be (from the place where it started).

  18. Relative motion • A motorboat is crossing a 350-m wide river moving 10 m/s relative to water. If current is 3 m/s east, how far down the stream will the boat end up when it reaches the opposite bank? What will the boat’s total displacement be? What will the boat’s velocity be relative to water? • (more than one way to solve!)

  19. Adding vectors that are NOT perpendicular

  20. Adding vectors algebraically

  21. Adding vectors

  22. Adding vectors

  23. RESOLVING VECTORS

  24. How fast must a truck travel to stay beneath an airplane that is moving 105 km/h at an angle of 25° to the ground?

  25. Practice finding components • 35 km/h 20o NE • 120 m 35o WN • 3.2 m/s2 40o SW • 65 km 70o ES X: 33 km/h Y: 12 km/h X: - 69 m Y: 99 m X: - 2.5 m/s2 Y: - 2.1 m/s2 X: 61 km Y: - 22km

  26. In groups, on big graph paper, illustrate the following • One of the holes on a golf course lies due east of the tee. A novice golfer flubs his tee shot so that the ball lands only 64 m directly northeast of the tee. He then slices the ball 30° south of east so that the ball lands in a sand trap 127 m away. Frustrated, the golfer then blasts the ball out of the sand trap, and the ball lands at a point 73 m away at an angle 27° north of east. At this point, the ball is on the putting green and 14.89 m due north of the hole. To his amazement, the golfer then sinks the ball with a single shot.

  27. Use algebraic formulas to find the x and y components of each displacement vector. Shot 1 x component _____________ y component _____________ Shot 2 x component _____________ y component _____________ Shot 3 x component _____________ y component _____________ Shot 4x component _____________ y component _____________

  28. Calculate • Find the total displacement (to the nearest meter) the golf ball traveled from the tee to the hole. Assume the golf course is flat. (Hint: Which component of each displacement vector contributes to the total displacement of the ball between the tee and the hole?)

  29. Adding vectors

  30. Adding vectors algebraically

  31. Example, p. 94, #1 • A football player runs directly down the field for 35 m before turning to the right at an angle of 25° from his original direction and running an additional 15 m before getting tackled. What is the magnitude and direction of the runner’s total displacement?

  32. Example 2, p 94, #4 • An airplane flying parallel to the ground undergoes two consecutive displacements. The first is 75 km 30.0° west of north, and the second is 155 km 60.0° east of north. What is the total displacement of the airplane? Answer: 171 km at 34° east of north

  33. Table hockey lab

  34. Projectile motion Free-falling while moving horizontally Moving in two directions at the same time

  35. Projectile motion

  36. Parabolic trajectory Vertical motion: with acceleration of -9.8 m/s2 and initial velocity vy and vertical displacement Δy Horizontal motion: constantvx and horizontal displacement Δx

  37. Projectile motion

  38. An object launched horizontally

  39. Find the initial speed of the bike

  40. Lab – Launching a Projectile Horizontally • Work in pairs • Each person should have his / her set of data • Each student turns in a report with his / her name on it.

  41. Projectile Launched at an angle Projectile has initial velocity in both directions

  42. Example • A football is kicked 22 m/s at 40o to the horizontal. Calculate the maximum height and horizontal range the football will reach before it falls down (providing no one catches it).

  43. 1st step:

  44. Example 2 (p.110, #35) • A place kicker must kick a football from a point 36.0 m from the goal. As a result of the kick, the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53° to the horizontal. • a. By how much does the ball clear or fall short of clearing the crossbar? • b. Does the ball approach the crossbar while still rising or while falling?

More Related