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# Parabolic motion

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### Parabolic motion

1. 1. PARABOLIC MOTION Created by Dr. Eng. Supriyanto, M.Sc Slide - 1Fundamental of Physics http://supriyanto.fisika.ui.edu
2. 2. Describing parabolic motion Parabolic motion refers to the motion of an object that is thrown, or projected, into the air at an angle. Parabolic motion is a combination of horizontal motion with constant horizontal velocity and vertical motion with a constant downward acceleration due to gravity.The vertical motion of a projected object is independent of its horizontal motion. The one common variable between the horizontal and vertical motions is time. Created by Dr. Eng. Supriyanto, M.Sc Slide - 2 Fundamental of Physics http://supriyanto.fisika.ui.edu
3. 3. Parabolic motionVelocities vector of horizontaland vertical motion Created by Dr. Eng. Supriyanto, M.Sc Slide - 3 Fundamental of Physics http://supriyanto.fisika.ui.edu
4. 4. Parabolic motion Horizontal  Motion of a ball rolling freely along a level surface  Horizontal velocity is ALWAYS constant Vertical  Motion of a freely falling object  Force due to gravity  Vertical component of velocity changes with time Parabolic  Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity Created by Dr. Eng. Supriyanto, M.Sc Slide - 4 Fundamental of Physics http://supriyanto.fisika.ui.edu
5. 5. Parabolic motion Horizontaland vertical motion Created by Dr. Eng. Supriyanto, M.Sc Slide - 5 Fundamental of Physics http://supriyanto.fisika.ui.edu
6. 6. Parabolic motionTime of flight is determined byvertical motion Created by Dr. Eng. Supriyanto, M.Sc Slide - 6 Fundamental of Physics http://supriyanto.fisika.ui.edu
7. 7. The bullet motion Created by Dr. Eng. Supriyanto, M.Sc Slide - 7 Fundamental of Physics http://supriyanto.fisika.ui.edu
8. 8. Angle for maximum distance Created by Dr. Eng. Supriyanto, M.Sc Slide - 8 Fundamental of Physics http://supriyanto.fisika.ui.edu
9. 9. Angle for maximum distance Created by Dr. Eng. Supriyanto, M.Sc Slide - 9 Fundamental of Physics http://supriyanto.fisika.ui.edu
10. 10. Projectile motionHorizontal component of velocity is constant over entire path! vx = v0x= v0cosα No acceleration in horizontal direction Created by Dr. Eng. Supriyanto, M.Sc Slide - 10 Fundamental of Physics http://supriyanto.fisika.ui.edu
11. 11. Projectile motionVertical component of velocity constantly changing due to gravitational acceleration in -y direction v0y --> 0 -> -v0y v0y = v0sinα Created by Dr. Eng. Supriyanto, M.Sc Slide - 11 Fundamental of Physics http://supriyanto.fisika.ui.edu
12. 12. Projectile motionAt the top of the trajectory: t = 1/2 of total time x = 1/2 of total horizontal range Created by Dr. Eng. Supriyanto, M.Sc Slide - 12 Fundamental of Physics http://supriyanto.fisika.ui.edu
13. 13. Projectile motion Horizontal motion of projectile: vx = v0cos α = constant ∆x = v0xt = (v0cos α)t Created by Dr. Eng. Supriyanto, M.Sc Slide - 13 Fundamental of Physics http://supriyanto.fisika.ui.edu
14. 14. Projectile motion Vertical motion of projectile: vy = v0sin α - gt ∆y = (v0sin α)t - 1/2gt2 vy2 = (v0sin α)2 - 2g∆y Created by Dr. Eng. Supriyanto, M.Sc Slide - 14 Fundamental of Physics http://supriyanto.fisika.ui.edu
15. 15. Projectile motion Combined 2D motion: v = (vx2 + vy2)1/2 tanθ = vy/vx θ = tan-1(vy/vx) -90 < θ < 90 Created by Dr. Eng. Supriyanto, M.Sc Slide - 15 Fundamental of Physics http://supriyanto.fisika.ui.edu
16. 16. Simulation#1 Created by Dr. Eng. Supriyanto, M.Sc Slide - 16 Fundamental of Physics http://supriyanto.fisika.ui.edu
17. 17. Simulation#2 Created by Dr. Eng. Supriyanto, M.Sc Slide - 17 Fundamental of Physics http://supriyanto.fisika.ui.edu
18. 18. Simulation#3 Created by Dr. Eng. Supriyanto, M.Sc Slide - 18 Fundamental of Physics http://supriyanto.fisika.ui.edu
19. 19. Exercise#1 Created by Dr. Eng. Supriyanto, M.Sc Slide - 19 Fundamental of Physics http://supriyanto.fisika.ui.edu
20. 20. Summary• A projectile is a body in free fall that is affect only by gravity and air resistance.• Projectile motion is analyzed in terms of its horizontal and vertical components. Vertical is affect by gravity• Factors that determine the height & distance of a projectile are; projection angle, projection speed, and relative projection height• The equation constant acceleration can be used to quantitatively analyze projectile motion. Created by Dr. Eng. Supriyanto, M.Sc Slide - 20 Fundamental of Physics http://supriyanto.fisika.ui.edu
21. 21. Exercise #2:1. A batter hits a ball at 35 with a velocity of 32 m/s. How high did the ball go? H = 17 m How long was the ball in the air? t = 3.8 s How far did the ball go? x = 98 m Created by Dr. Eng. Supriyanto, M.Sc Slide - 21 Fundamental of Physics http://supriyanto.fisika.ui.edu
22. 22. Exercise #2:2. While driving down a road a bad guy shoots a bullet straight up into the air. If there was no air resistance where would the bullet land – in front, behind, or on him?• If air resistance present, bullet slows and lands behind.• No air resistance, the Vx doesn’t change and bullet lands on him. Created by Dr. Eng. Supriyanto, M.Sc Slide - 22 Fundamental of Physics http://supriyanto.fisika.ui.edu
23. 23. Exercise #2:3. A truck (v = 11.2 m/s) turned a corner too sharp and lost part of the load. A falling box will break if it hits the ground with a velocity greater than 15 m/s. The height of the truck bed is 1.5 m. Will the box break? v = 12 m/s, No it doesn’t break Created by Dr. Eng. Supriyanto, M.Sc Slide - 23 Fundamental of Physics http://supriyanto.fisika.ui.edu
24. 24. Exercise #2:4. A meatball with v = 5.0 m/s rolls off a 1.0 m high table. How long does it take to hit the floor? t = 0.45 s What was the velocity when it hit? v = 6.7 m/s @ 42° Created by Dr. Eng. Supriyanto, M.Sc Slide - 24 Fundamental of Physics http://supriyanto.fisika.ui.edu