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Lecture 10: Vectors, Projectile Motion Please sit in the first six rows Exam I Average = 83 10 9 8 7 6 5 4 3 2 1 0 A B C D F Vector Components Ax A cos y Ay A sin A Ay θ Ax x Ax A cos y A cos Ay A sin Ay θ φ Ax < 0 x Adding vectors numerically C A B Cx Ax Bx C y Ay By Also called algebraic addition What would subtraction look like? Scalar multiplication? A A = 15 m B = 25 m 300 200 B Find Ax, Ay, Bx, By C A B Cx , C y , C ,C 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 The vector has length 4.0 units. What are the x- and y-components of this vector? The vector has length 4.0 units. x- and y-components ? 2. 0 20% -3 .5 ,- 20% 3. 5 20% 2. 0, - 20% -3 .5 ,2 .0 20% 2. 0, 3. 5 3.5, 2.0 2.0, 3.5 -3.5, 2.0 2.0, -3.5 -3.5, -2.0 3. 5, 2. 0 1. 2. 3. 4. 5. Velocity as a vector d d v , same direction as d t t dr ( x, y ) dt dx(t ) vx dt dy (t ) vy dt y Particle moves from 1 to 2 in time Δt. Draw the velocity vector. 1 2 x Acceleration as a vector v f vi v dv a t f ti t dt dvx ax , dt ay dv y dt Note that unless object is moving in a straight line, a is not in the direction of v 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 Motion on a Ramp In the Soapbox Derby, young participants build cars with very lowfriction 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 Projectile Motion • Projectile launched at an angle θ above the horizontal with an initial velocity of vi. y • vix , viy vi θ x Projectile motion x and y motion independent ax 0 vx (t ) vix x(t ) xi vixt a y g v y (t ) viy g * t 1 2 y (t ) yi viy gt 2 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? Circular Motion There is an acceleration because the velocity is changing direction. Slide 3-35 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 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