# Lect_05 - ACT Alice and Bob Lecture 5 2D and 3D motion...

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Lecture 5 2D and 3D motion ACT: Alice and Bob 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 A and B , respectively. Which of the following is true? Alice Bob 0 0 A B A) A < B B) A = B C) A > B y 0 = h 2 = 0 2 –2 gh same for both! + 0 or – 0 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: () rt G x (3 s ) = G (1 s ) = G trajectory Displacement: ( ) rrt trt ∆= + ∆ − GG G final initial or rr r GG G Velocity Velocity = G G Average: t  == = =   G G Instantaneous: , , xyz dy dr dx dz vv dt G is always tangent to the trajectory. v G s ) vt = G s ) = G

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Acceleration Acceleration •A v e r a g e : • Instantaneous: = G G v a t  == = =   G G ,, y xz xyz dv aa dt 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? x 1s 2s 3s 4s A) = 0, y > 0 B) > 0, y > 0 C) < 0, y = 0 Note: Both the speed and the direction of velocity are changing! 1s 2s 3s 4s (1) (1) (2) (3) (1) (3) The big new thing in 2D: changes in direction Change in speed; parallel to v Change in direction; perpendicular to v ˆˆ () dv d vv dv dv vv v a dt dt dt dt = = + G G G An object can move at constant speed and still have a 0! This didn’t happen in 1D!! vt G t +∆ G v G a G G t tt + ∆ t G Graphically: Imagine an object moving along the following trajectory at constant speed. Take the positions at times and and find the average acceleration between them:
In 2 (or 3) dimensions, acceleration can occur both parallel to velocity or perpendicular to it

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Lect_05 - ACT Alice and Bob Lecture 5 2D and 3D motion...

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