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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Presentation transcript:

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

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

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

Great Suggestions for Success Mechanics Lecture 1, Slide 4

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.

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

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

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

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

Catch problem responses Mechanics Lecture 1, Slide 10

Catch 2 responses Mechanics Lecture 1, Slide 11

Soccer Kick responses Mechanics Lecture 1, Slide 12

Cannonball Responses Mechanics Lecture 1, Slide 13

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

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

Homework Solutions-Baseball Mechanics Lecture 1, Slide 16

Homework Solutions-Baseball Mechanics Lecture 1, Slide 17

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

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:

Homework Solutions-Baseball Stadium Mechanics Lecture 1, Slide 20

Homework Hints-Catch Mechanics Lecture 1, Slide 21

Homework Hints-Catch Mechanics Lecture 1, Slide 22

Homework Hints-Catch Mechanics Lecture 1, Slide 23

Homework Solutions-Catch Mechanics Lecture 1, Slide 24

Homework Solutions-Catch Mechanics Lecture 1, Slide 25

Homework Solutions-Catch Mechanics Lecture 1, Slide 26

Homework Hints-Catch 2 Mechanics Lecture 1, Slide 27

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.

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

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

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

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

Homework Solutions-Catch Mechanics Lecture 1, Slide 33

Homework Hints-Catch Mechanics Lecture 1, Slide 34

Homework Hints-Catch 2 Mechanics Lecture 1, Slide 35

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.

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

Homework Hints – soccer kick Mechanics Lecture 1, Slide 38

Homework Solutions– soccer kick Mechanics Lecture 1, Slide 39

Homework Solutions – soccer kick Mechanics Lecture 1, Slide 40

Homework Solutions - Cannonball Mechanics Lecture 1, Slide 41

Cannonball Solutions Mechanics Lecture 1, Slide 42

Cannonball- Solutions Mechanics Lecture 1, Slide 43

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

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

Trigonometric Identity for range equation Mechanics Lecture 2, Slide

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

Hyperphysics-Trajectories Mechanics Lecture 1, Slide 48