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

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Vector Components y x A AxAx AyAy θ

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y x A x < 0 AyAy θ φ

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

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A B 30 0 20 0 A = 15 m B = 25 m Find A x, A y, B x, B y

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Examples Slide 3-27 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?

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

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The vector has length 4.0 units. x- and y-components ? 1.3.5, 2.0 2.2.0, 3.5 3.-3.5, 2.0 4.2.0, -3.5 5.-3.5, -2.0

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Velocity as a vector

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

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

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Slide 3-28 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 v i and v f ?

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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

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Projectile Motion Projectile launched at an angle θ above the horizontal with an initial velocity of v i. v ix, v iy y x vivi θ

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Projectile motion x and y motion independent

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

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

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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

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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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Factor P 16 8(8-5ab) 4(d² + 4) 3rs(2r – s) 15cd(1 + 2cd) 8(4a² + 3b²)

Factor P 16 8(8-5ab) 4(d² + 4) 3rs(2r – s) 15cd(1 + 2cd) 8(4a² + 3b²)

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