(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!
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
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
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:
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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