(5) 2D and 3D Motion

(5) 2D and 3D Motion - Lecture 5 2D and 3D motion ACT:...

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Lecture 5 2D and 3D motion
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ACT: Alice and Bob Alice and Bob stand at the top of a cliff of height h. Both throw a ball with initial speed v 0 , Alice straight up and Bob straight down. The speed of the balls when they hit the ground are v A and v B , respectively. Which of the following is true? Alice Bob v 0 v 0 v A v B A) v A < v B B) v A = v B C) v A > v B y – y 0 = h v 2 0 2 – 2gh same for both!
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2D (and 3D) motion Now we need vectors to indicate position, velocity and acceleration, but the definitions we use in 1D are pretty much the same. Position: ( ) r t r x y ( 3 s) r t = r ( 1 s) r t = r trajectory Displacement: ( ) ( ) r r t t r t = + ∆ - r r r ( 29 f inal init ial or r r r = - r r r Δ r
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Velocity = r r Average: r v t = = = = r r I nst ant aneous: , , x y z dy dr dx dz v v v v dt r is always t angent t o t he t r aj ect or y. v v r ( 1 s) v t = r ( 3 s) v t = r
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Acceleration Average: Instantaneous: = r r v a t = = = = r r , , y x z x y z dv a a a a dt
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ACT: Acceleration Shown below are the trajectory of a moving object and the snapshots taken every second. Which of the following is true about the components of the acceleration? y x 1s 2s 3s 4s A) a x = 0, a y > 0 B) a x > 0, a y C) a x < 0, a y = 0
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Note: Both the speed and the direction of velocity are changing! y x 1s 2s 3s 4s v(1) v(2) v(3) Δ v
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The big new thing in 2D: changes in direction Change in speed; parallel to v Change in direction; perpendicular to v ˆ ˆ ( ) ˆ ˆ dv d vv dv dv v vv a v v dt dt dt dt = = = = + r r r An object can move at constant speed and still have a 0! This didn’t happen in 1D!! r ( ) v t t + ∆ r v r a r r t t t + ∆ ( ) v t t + ∆ r Graphically: Imagine an object moving along the following trajectory at constant speed. Take the positions at times t and Δ t and find the average acceleration between them:
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In 2 (or 3) dimensions, acceleration can
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This note was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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(5) 2D and 3D Motion - Lecture 5 2D and 3D motion ACT:...

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