Parabolic motion refers to the motion of an object thrown or projected at an angle, which involves independent horizontal and vertical motion combined. The horizontal motion has constant velocity, while the vertical motion is affected by gravity and results in changing velocity. The time of flight of the object is determined by its vertical motion. Key factors that determine the height and distance traveled are the projection angle, speed, and initial height.

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
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Fundamental of Physics http://supriyanto.fisika.ui.edu

7. The bullet motion
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8. Angle for maximum distance
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9. Angle for maximum distance
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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
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17. Simulation#2
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Fundamental of Physics http://supriyanto.fisika.ui.edu

18. Simulation#3
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19. Exercise#1
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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