1. Slide - 1 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu PARABOLIC MOTION

2. Slide - 2 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Parabolic motion refers to the motion of an object that is thrown, or projected, into the air at an angle. Describing parabolic motion 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.

3. Slide - 3 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Velocities vector of horizontal and vertical motion Parabolic motion

4. Slide - 4 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Parabolic motion HHHHorizontal MMotion of a ball rolling freely along a level surface HHorizontal velocity is ALWAYS constant VVVVertical MMotion of a freely falling object FForce due to gravity VVertical component of velocity changes with time PPPParabolic PPath traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

5. Slide - 5 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Horizontal and vertical motion Parabolic motion

6. Slide - 6 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Time of flight is determined by vertical motion Parabolic motion

7. Slide - 7 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu The bullet motion

8. Slide - 8 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Angle for maximum distance

9. Slide - 9 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Angle for maximum distance

10. Slide - 10 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion Horizontal component of velocity is constant over entire path! v x = v 0x = v 0 cos  No acceleration in horizontal direction

11. Slide - 11 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion Vertical component of velocity constantly changing due to gravitational acceleration in -y direction v 0y --> 0 -> -v 0y v 0y = v 0 sin 

12. Slide - 12 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion At the top of the trajectory: t = 1/2 of total time x = 1/2 of total horizontal range

13. Slide - 13 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion v x = v 0 cos  = constant  x = v 0x t = (v 0 cos  t Horizontal motion of projectile:

14. Slide - 14 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion Vertical motion of projectile: v y = v 0 sin  - gt  y = (v 0 sin  t - 1/2gt 2 v y 2 = (v 0 sin  2 - 2g  y

15. Slide - 15 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Projectile motion Combined 2D motion: v = (v x 2 + v y 2 ) 1/2 tan  = v y /v x  = tan -1 (v y /v x ) -90 <  < 90

16. Slide - 16 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Simulation#1

17. Slide - 17 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Simulation#2

18. Slide - 18 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Simulation#3

19. Slide - 19 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu Exercise#1

20. Slide - 20 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu 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.

21. Slide - 21 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu 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

22. Slide - 22 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu 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 V x doesn’t change and bullet lands on him.

23. Slide - 23 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu 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

24. Slide - 24 Fundamental of Physics Created by Dr. Eng. Supriyanto, M.Sc http://supriyanto.fisika.ui.edu 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°