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UNIT 2 Two Dimensional Motion And Vectors

UNIT 2 Two Dimensional Motion And Vectors. ConcepTest 3.1a Vectors I. 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions

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UNIT 2 Two Dimensional Motion And Vectors

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  1. UNIT 2Two Dimensional Motion And Vectors

  2. ConcepTest 3.1a Vectors I 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B?

  3. ConcepTest 3.1a Vectors I 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B? The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sum to come out to zero. You can prove this with the tip-to-tail method.

  4. Monday September 19th Introduction of Vectors

  5. TODAY’S AGENDA Monday, September 19 • Intro to Vectors • Mini-Lesson: Properties of Vectors • Hw: Worksheet Pg. 13-14 UPCOMING… • Tues: Vector Operations • Wed: More Vector Operations • Thurs: Problem Quiz 1 Vectors • Mini-Lesson: Projectile Motion

  6. Notating Vectors Text books usually write vector names in bold. This is how you notate a vector… You would write the vector name with an arrow on top. This is how you draw a vector…

  7. Vector Angle Ranges y Quadrant II 90˚< θ< 180˚ Quadrant I 0˚< θ< 90˚ θ θ • x θ θ Quadrant IV 270˚< θ< 360˚ Quadrant III 180˚< θ< 270˚

  8. Direction of Vectors What angle range would this vector have? What would be the exact angle and how would you determine it? Between 180˚ and 270˚ θ • x θ Between -270˚ and -180˚

  9. Magnitude of Vectors The best way to determine the magnitudeof a vector is to measure its length. The length of the vector is proportional to the magnitude (or size) of the quantity it represents.

  10. Sample Problem

  11. Equal Vectors

  12. Inverse Vectors

  13. Right Triangle Trigonometry

  14. Pythagorean Theorem Hypotenuse2 = Opposite side2 + Adjacent side2

  15. Basic Trigonometric Functions

  16. Trigonometric Inverse Functions

  17. Trigonometry Refresher: y x q To find the resultant, To find the angle, q

  18. Sample Problem Tree tan 50˚ = width/100 m width = (100 m) tan 50˚ 155 m 119 m width = 119 m R2 = (119 m)2 + (100 m)2 50˚ R = 155 m 100 m

  19. Sample Problem You are standing at the very top of a tower and notice that in order to see a manhole cover on the ground 50.0 meters from the base of the tower, you must look down at an angle 75.0˚ below the horizontal. If you are 1.80 m tall, how high is the tower? tan 75.0˚= height(eye) / 50.0 m 75˚ height(eye) = (50.0 m) tan 75.0˚ height(eye) = 187 m height(building) = 187 m – 1.80 m 75˚ height(building) = 185 m 50 m

  20. END

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