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Vectors and 2d-Kinematics Continued

Vectors and 2d-Kinematics Continued. Relevant Equations How to use them Homework Hints. Hyperphysics -Trajectories. http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html. Projectile Motion Quantities. Initial velocity  speed,angle. Maximum Height of trajectory, h= y max. “Hang Time”

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Vectors and 2d-Kinematics Continued

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  1. Vectors and 2d-KinematicsContinued Relevant Equations How to use them Homework Hints

  2. Hyperphysics-Trajectories http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

  3. Projectile Motion Quantities Initial velocity speed,angle Maximum Height of trajectory, h=ymax “Hang Time” Time of Flight, tf Range of trajectory, D Height of trajectory at arbitrary x,t

  4. Hyperphysics-Trajectories

  5. Maximum Height of Trajectory Height of trajectory,h=ymax

  6. Time of Flight

  7. Time of Flight, “Hang Time”

  8. Hyperphysics-Trajectories

  9. Range of trajectory

  10. Angle for Maximum Range MAXIMUM range OCCURS AT 450

  11. Will it clear the fence

  12. Height of Trajectory at time t or position x Height of trajectory, y(t) Height of trajectory, y(x)

  13. Projectile Trajectory Equations Maximum height Time of Flight (“Hang Time”) Range of trajectory Height of trajectory as f(t) , y(t) Height of trajectory as f(x), y(x)

  14. Where will it land?

  15. Launch Velocity-Given R and 

  16. Launch Angle

  17. Launch Velocity –Given R and h

  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 x 3 m D y-direction voy = vo sin(30o) = 15 m/s y = yo + voyt + ½ at2 3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t2 t = 2.8 s or t = 0.22 s. x-direction vox = vo cos(30o) = 26 m/s D = xo + vox t + ½ at2 = 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2 = 72.8 m Illini Kicks 70 yard Field Goal

  19. Homework Hints-Baseball

  20. Homework Hints- Baseball Stadium Wall

  21. Homework Hints – Stadium Wall Calculate time to reach wall using vx: Calculate y position at time to reach wall:

  22. Homework Hints-Catch

  23. Homework Hints-Catch

  24. Homework Hints-Catch

  25. Homework Hints-Catch 2

  26. Homework Hints-Catch 2 Vxis constant ! v Kinetic energy should be same as when ball was thrown. Y-component of velocity would be downward.

  27. Homework Hints-Catch 2 Same conditions as before

  28. Homework Hints – Soccer Kick & Cannonball

  29. Homework Hints – Soccer Kick & Cannonball

  30. Homework Hints – Soccer Kick & Cannonball

  31. Trigonometric Identity for range equation http://mathworld.wolfram.com/Sine.html http://mathworld.wolfram.com/Cosine.html

  32. Trigonometric Identities relating sum and products List of trigonometric identities

  33. Question 2

  34. Question 2

  35. Hyperphysics-Trajectories http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

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