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Mechanics Lecture 2, Slide 1 Vectors and 2d-Kinematics Continued Comments on Homework Summary of Vectors and 2-d Kinematics Homework Solutions

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Homework Results Vectors and 2-d kinematics Mechanics Lecture 1, Slide 2 Average=87% No attempt = 14 Awesome Job! See Me or TAs

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Homework 1 results Mechanics Lecture 1, Slide 3 Average=62.5% Among those who made an attempt Average=74.7%

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Great Suggestions for Success Mechanics Lecture 1, Slide 4

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Questions/Suggestions Mechanics Lecture 1, Slide 5 Each component can be treated separately. Remember that they are component of a vector Kinematic equations for displacement,velocity and acceleration are the source for the derived equations. For this situation the horizontal component of the velocity remains constant. The vertical component of velocity changes due to the gravitational acceleration.

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Mechanics Lecture 2, Slide 6 Vectors and 2d-kinematics – Main Points

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Mechanics Lecture 2, Slide 7 Vectors and 2d-kinematics – Main Points

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Vectors and 2d-kinematics Fundamental Equations Mechanics Lecture 2, Slide 8

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Source of Projectile Trajectory Equations Mechanics Lecture 1, Slide 9 Horizontal Vertical Boring

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Catch problem responses Mechanics Lecture 1, Slide 10

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Catch 2 responses Mechanics Lecture 1, Slide 11

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Soccer Kick responses Mechanics Lecture 1, Slide 12

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Cannonball Responses Mechanics Lecture 1, Slide 13

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Ballistic Projectile Motion Quantities Mechanics Lecture 2, Slide 14 Initial velocity speed,angle Maximum Height of trajectory, h=y max Range of trajectory, D Height of trajectory at arbitrary x,t “Hang Time” Time of Flight, t f

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Derived Projectile Trajectory Equations Mechanics Lecture 1, Slide 15 Height of trajectory as f(x), y(x) Height of trajectory as f(t), y(t) Range of trajectory Time of Flight (“Hang Time”) Maximum height

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Homework Solutions-Baseball Mechanics Lecture 1, Slide 16

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Homework Solutions-Baseball Mechanics Lecture 1, Slide 17

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Homework Hints- Baseball Stadium Wall Mechanics Lecture 1, Slide 18

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Homework Hints – Stadium Wall Mechanics Lecture 1, Slide 19 Calculate time to reach wall using v x : Calculate y position at time to reach wall:

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Homework Solutions-Baseball Stadium Mechanics Lecture 1, Slide 20

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Homework Hints-Catch Mechanics Lecture 1, Slide 21

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Homework Hints-Catch Mechanics Lecture 1, Slide 22

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Homework Hints-Catch Mechanics Lecture 1, Slide 23

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Homework Solutions-Catch Mechanics Lecture 1, Slide 24

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Homework Solutions-Catch Mechanics Lecture 1, Slide 25

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Homework Solutions-Catch Mechanics Lecture 1, Slide 26

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 27

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 28 v V x is constant ! Kinetic energy should be same as when ball was thrown. Y- component of velocity would be downward.

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 29 Same conditions as before

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Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 30

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Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 31

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Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 32

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Homework Solutions-Catch Mechanics Lecture 1, Slide 33

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Homework Hints-Catch Mechanics Lecture 1, Slide 34

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 35

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Homework Solutions-Catch 2 Mechanics Lecture 1, Slide 36 v V x is constant ! Kinetic energy should be same as when ball was thrown. Y- component of velocity would be downward.

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Homework Solutions-Catch 2 Mechanics Lecture 1, Slide 37 Same conditions as before

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Homework Hints – soccer kick Mechanics Lecture 1, Slide 38

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Homework Solutions– soccer kick Mechanics Lecture 1, Slide 39

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Homework Solutions – soccer kick Mechanics Lecture 1, Slide 40

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Homework Solutions - Cannonball Mechanics Lecture 1, Slide 41

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Cannonball Solutions Mechanics Lecture 1, Slide 42

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Cannonball- Solutions Mechanics Lecture 1, Slide 43

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Mechanics Lecture 2, Slide 44 Vectors and 2d-kinematics – Main Points

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Mechanics Lecture 2, Slide 45 Time spend in the air depends on the maximum height Maximum height depends on the initial vertical velocity v train car

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Trigonometric Identity for range equation Mechanics Lecture 2, Slide 46 http://mathworld.wolfram.com/Cosine.html http://mathworld.wolfram.com/Sine.html

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Trigonometric Identities relating sum and products Mechanics Lecture 2, Slide 47 List of trigonometric identities

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Hyperphysics-Trajectories Mechanics Lecture 1, Slide 48 http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

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