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

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

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

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

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

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

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

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

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

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

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

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. 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. 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. 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. 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