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Lecture 10: Vectors, Projectile Motion

Lecture 10: Vectors, Projectile Motion. Please sit in the first six rows. Vector Components. y. A. A y. θ. x. A x. y. A y. θ. φ. x. A x < 0. Adding vectors numerically. Also called algebraic addition What would subtraction look like? Scalar multiplication?. A = 15 m B = 25 m.

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Lecture 10: Vectors, Projectile Motion

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  1. Lecture 10: Vectors, Projectile Motion Please sit in the first six rows

  2. Vector Components y A Ay θ x Ax

  3. y Ay θ φ x Ax < 0

  4. Adding vectors numerically Also called algebraic addition What would subtraction look like? Scalar multiplication?

  5. A = 15 m B = 25 m A 300 200 B Find Ax, Ay, Bx, By

  6. Examples The labeled vectors each have length 4 units. For each vector, what is the component parallel to the ramp? The labeled vectors each have length 4 units. For each vector, what is the component perpendicular to the ramp? Slide 3-27

  7. The vector has length 4.0 units.What are the x- and y-components of this vector?

  8. The vector has length 4.0 units.x- and y-components ? • 3.5, 2.0 • 2.0, 3.5 • -3.5, 2.0 • 2.0, -3.5 • -3.5, -2.0

  9. Velocity as a vector

  10. y Particle moves from 1 to 2 in time Δt. Draw the velocity vector. 1 2 x

  11. Acceleration as a vector Note that unless object is moving in a straight line, a is not in the direction of v

  12. The diagram below shows two successive positions of a particle; it’s a segment of a full motion diagram. Which of the acceleration vectors best represents the acceleration between vi and vf?   Slide 3-28

  13. Motion on a Ramp In the Soapbox Derby, young participants build cars with very low-friction wheels in which they roll down a hill. Cars racing on the track at Akron’s Derby Downs, where the national championship is held, begin on a 55 ft section of the track that is tipped 13° from the horizontal. What is the maximum possible acceleration of a car moving down this stretch of track? If a car starts from rest and accelerates at this rate for the full 55 ft, how fast will it be moving? Slide 3-30

  14. Projectile Motion • Projectile launched at an angle θ above the horizontal with an initial velocity of vi. • vix , viy y vi θ x

  15. Projectile motionx and y motion independent

  16. Problem 3:28 A ball with a horizontal speed of 1.25 m/s rolls off a bench 1.00m above the floor. How long will it take the ball to hit the floor? How far from a point directly below the edge of the bench will the ball hit the floor?

  17. Circular Motion There is an acceleration because the velocity is changing direction. Slide 3-35

  18. Circular Motion Old vinyl records are 12" in diameter, and spin at 33⅓ rpm when played. What’s the acceleration of a point on the edge of the record? Two friends are comparing the acceleration of their vehicles. Josh owns a Ford Mustang, which he clocks as doing 0 to 60 mph in a time of 5.6 seconds. Josie has a Mini Cooper that she claims is capable of a higher acceleration. When Josh laughs at her, she proceeds to drive her car in a tight circle at 13 mph. Which car experiences a higher acceleration? Slide 3-36

  19. Homework for Today Reading: 3: 1-6 Problems: 3: CQ1, CQ3, MC19, MC20, 1, 2, 6, 7, 9, 12 MONDAY Reading: 3: 7-8 • Problems: 3: CQ10, MC18, 13, 14, 16, 18, 21, 23, 26, 28, 30, 33

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