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Mechanics Lecture 2, Slide 1 Vectors and 2d-Kinematics Continued Relevant Equations How to use them Homework Hints

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Hyperphysics-Trajectories Mechanics Lecture 1, Slide 2 http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

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Projectile Motion Quantities Mechanics Lecture 2, Slide 3 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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Hyperphysics-Trajectories Mechanics Lecture 1, Slide 4

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Maximum Height of Trajectory Mechanics Lecture 2, Slide 5 Height of trajectory,h=y max

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Time of Flight Mechanics Lecture 1, Slide 6

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Time of Flight, “Hang Time” Mechanics Lecture 2, Slide 7

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Hyperphysics-Trajectories Mechanics Lecture 1, Slide 8

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Range of trajectory Mechanics Lecture 2, Slide 9

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Angle for Maximum Range Mechanics Lecture 2, Slide 10 MAXIMUM range OCCURS AT 45 0

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Will it clear the fence Mechanics Lecture 1, Slide 11

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Height of Trajectory at time t or position x Mechanics Lecture 2, Slide 12 Height of trajectory, y(x) Height of trajectory, y(t)

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Projectile Trajectory Equations Mechanics Lecture 1, Slide 13 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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Where will it land? Mechanics Lecture 1, Slide 14

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Launch Velocity-Given R and Mechanics Lecture 1, Slide 15

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Launch Angle Mechanics Lecture 1, Slide 16

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Launch Velocity –Given R and h Mechanics Lecture 1, Slide 17

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Mechanics Lecture 2, Slide 18 Field Goal Example A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y-direction v oy = v o sin(30 o ) = 15 m/s y = y o + v oy t + ½ at 2 3 m = 0 m + (15 m/s) t – ½ (9.8 m/s 2 ) t 2 t = 2.8 s or t = 0.22 s. x-direction v ox = v o cos(30 o ) = 26 m/s D = x o + v ox t + ½ at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 = 72.8 m D 3 m y x Illini Kicks 70 yard Field Goal

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Homework Hints-Baseball Mechanics Lecture 1, Slide 19

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Homework Hints- Baseball Stadium Wall Mechanics Lecture 1, Slide 20

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Homework Hints – Stadium Wall Mechanics Lecture 1, Slide 21 Calculate time to reach wall using v x : Calculate y position at time to reach wall:

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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 Hints-Catch Mechanics Lecture 1, Slide 24

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 25

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Homework Hints-Catch 2 Mechanics Lecture 1, Slide 26 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 27 Same conditions as before

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Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 28

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Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 29

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

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Trigonometric Identity for range equation Mechanics Lecture 2, Slide 31 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 32 List of trigonometric identities

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Question 2 Mechanics Lecture 2, Slide 33

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Question 2 Mechanics Lecture 2, Slide 34

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Hyperphysics-Trajectories Mechanics Lecture 1, Slide 35 http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

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