PARABOLIC MOTION
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 1
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.
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 2
Parabolic motion
Velocities vector of
horizontal
and vertical motion
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 3
Parabolic motion

Horizontal
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Vertical

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Motion of a ball rolling freely along a
level surface
Horizontal velocity is ALWAYS constant
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
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 4
Parabolic motion
Horizontal
and vertical motion
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 5
Parabolic motion
Time of flight
is determined
by
vertical motion
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 6
The bullet motion
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 7
Angle for maximum distance
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 8
Angle for maximum distance
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 9
Projectile motion
Horizontal component of velocity is constant over entire path!
vx = v0x= v0cosa
No acceleration in horizontal direction
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 10
Projectile motion
Vertical component of velocity constantly changing due to
gravitational acceleration in -y direction
v0y --> 0 -> -v0y
v0y = v0sina
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 11
Projectile motion
At the top of the trajectory:
t = 1/2 of total time
x = 1/2 of total horizontal range
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 12
Projectile motion
Horizontal motion of projectile:
vx = v0cos a = constant
Dx = v0xt = (v0cos a)t
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 13
Projectile motion
Vertical motion of projectile:
vy = v0sin a - gt
Dy = (v0sin a)t - 1/2gt2
vy2 = (v0sin a)2 - 2gDy
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 14
Projectile motion
Combined 2D motion:
v = (vx2 + vy2)1/2
tanq = vy/vx
q = tan-1(vy/vx)
-90 < q < 90
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 15
Simulation#1
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 16
Simulation#2
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 17
Simulation#3
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 18
Exercise#1
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 19
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.
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 20
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
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 21
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.
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 22
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
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 23
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°
Fundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Slide - 24