Parabolic motion

1. Slide - Slide - 11 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
PARABOLIC MOTION

2. Slide - Slide - 22 Fundamental of PhysicsFundamental 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 - Slide - 33 Fundamental of PhysicsFundamental 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 - Slide - 44 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Parabolic motion

HorizontalHorizontal

Motion of a ball rolling freely along a
level surface

Horizontal velocity is ALWAYS constant

VerticalVertical

Motion of a freely falling object

Force due to gravity

Vertical component of velocity changes
with time

ParabolicParabolic

Path traced by an object accelerating
only in the vertical direction while
moving at constant horizontal velocity

5. Slide - Slide - 55 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Horizontal
and vertical motion
Parabolic motion

6. Slide - Slide - 66 Fundamental of PhysicsFundamental 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 - Slide - 77 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
The bullet motion

8. Slide - Slide - 88 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Angle for maximum distance

9. Slide - Slide - 99 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Angle for maximum distance

10. Slide - Slide - 1010 Fundamental of PhysicsFundamental 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
cosa
No acceleration in horizontal direction

11. Slide - Slide - 1111 Fundamental of PhysicsFundamental 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
sina

12. Slide - Slide - 1212 Fundamental of PhysicsFundamental 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 - Slide - 1313 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Projectile motion
v
x
= v
0
cos a = constant
Dx = v
0x
t = (v
0
cos a)t
Horizontal motion of projectile:

14. Slide - Slide - 1414 Fundamental of PhysicsFundamental 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 a - gt
Dy = (v
0
sin a)t - 1/2gt
2
v
y
2
= (v
0
sin a)
2
- 2gDy

15. Slide - Slide - 1515 Fundamental of PhysicsFundamental 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
tanq = v
y
/v
x
q = tan
-1
(v
y
/v
x
)
-90 < q < 90

16. Slide - Slide - 1616 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Simulation#1

17. Slide - Slide - 1717 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Simulation#2

18. Slide - Slide - 1818 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Simulation#3

19. Slide - Slide - 1919 Fundamental of PhysicsFundamental of Physics
Created by Dr. Eng. Supriyanto, M.Sc
http://supriyanto.fisika.ui.edu
Exercise#1

20. Slide - Slide - 2020 Fundamental of PhysicsFundamental 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 - Slide - 2121 Fundamental of PhysicsFundamental 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 - Slide - 2222 Fundamental of PhysicsFundamental 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 - Slide - 2323 Fundamental of PhysicsFundamental 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 - Slide - 2424 Fundamental of PhysicsFundamental 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°