1. Free Fall

2. Projectile Motion – free fall, but not vertical

3. Free Fall:
Used to describe the motion of any object that
is moving _____________________________
the only force acting is ________________
no _____________________ , which is a good
approximation if object moves ____________
motion can be _________________ or in an arc
known as a ____________________
the results are independent of ___________
All of the equations of __________________can
used as long as you use:
a = _______ = ___________________= ____________
= _____________on or near Earth’s surface
for the time the object is in ________________ .
freely through a vacuum.
gravity
air resistance
slowly
up or down
parabola
mass
kinematics -g
9.81 m/s2 down
-9.81 m/s2
constant
free fall

5. Free fall applies to an object that is…
fired up or
down _____
__________:
dropped
___________
from rest:
_________
down:
thrown at
an angle
fired
______________:
fired
_______up:
horizontally
in flight
…only for the time while it is ________________.
In all cases:
d is _________________if the object ends up
__________ the point where it started.
2. d is _________________if the object ends up
3. v is positive if object is going ________________
4. v is negative if object is going ________________
5. a is _________________________
positive
above
negative
below
up or right
down or left
always m/s2

7. ______________ motion
A. Dropped Objects.
Vertical
Ex 1: A ball is dropped. How far will it fall
in 3.5 seconds?
equation:
given:
d = vit ½ at2
a = m/s2
d = 0t ½(-9.81)(3.5)2
vi = 0
t = 3.5 s
d = ½(-9.81)(12.25)
unknown:
d = ?
d = -60. m

8. Ex. Harry Potter falls freely 99 meters from rest.
How much time will he be in the air?
equation:
given:
d = vit ½ at2
a = m/s2
-99 = 0t ½(-9.81)(t)2
vi = 0
d = -99 m
-99 = t2
unknown:
t2 = 20.2
t = ?
t = 4.5 s

9. Ex. Mr. Siudy falls off a cliff. What will be his
velocity at the instant he hits ground if he falls for
1.3 seconds?
equation:
given:
a = m/s2
vf = vi + at
vi = 0
t= 1.3 s
vf = 0 + (-9.81)(1.3)
unknown:
vf = ?
vf = -13 m/s
A rock that has half the mass of Mr. Siudy
is dropped at the same time. If it falls for the
same time, what will its final speed be?
Which will hit the ground first?
same
neither

10. B. Objects Fired Up or Down.
Ex. A ball is tossed up with an initial speed of
24 meters per second. How high up will it go? vf
given:
equation:
a = m/s2
vf2 = vi2 + 2ad
vi = 24 m/s
0 = (-9.81)d
vf = 0
-576 = -19.6d vi
unknown:
29.4 m = d
d= ?
What total distance will it travel before it lands?
58.8 m
What will be its resultant displacement
when it lands?
0. m

11. For a ball fired or thrown straight up:
_______ d each second on way up
______ d each second on way down
tup = _____________
ttotal = _______ = __________
vtop =__________
6. atop= __________
7. speedup = _______________
If object falls back to its original
height, then: vf=______
v = 0
less
more
tdown
2tup
2tdown
-9.81 m/s2
speeddown vi
-vi vf
going up
coming
down

12. Ex. Mr. Siudy is fired directly up with an
initial speed of 55 meters per second. How long
will he be in the air?
given:
equation:
a = m/s2
a = Δv/t
a = (vf – vi)/t
vi = 55 m/s vi
-9.81 = (-55 – 55)/t
vf = -55 m/s
unknown:
t = (-110)/-9.81 vf
t= ?
t = 11 s
How much time did he spend going up?
t = 5.5 s

13. Ex. A shot put is thrown straight down from
a cliff with an initial speed of 15 m/s. How far
must it fall before it reaches a speed of 35 m/s?
given:
equation:
a = m/s2
vf2 = vi2 + 2ad
vi = -15 m/s
(-35)2 = (-15)2 + 2(-9.81)d
vf = -35 m/s
= -19.6d
unknown:
1000 = -19.6d
d= ?
1000/(-19.6) = d
-51 m = d

14. C. Graphical analysis: use a ≈ _____________
-10 m/s2
C. Graphical analysis: use a ≈ _____________
Ex: ball dropped from rest
v (m/s) t
(s) d
(m) v
(m/s) a
(m/s2) 1 2 3
t (s)
-10
5 m
15 m 1 -5
-10
-10
-10
25 m 2
-20
-20
-10
35 m
-20 3
-45
-30
-10
-30 4
-80
-40
-10
-40

15. See any patterns? time total d velocity 0 s 0 m 0 m/s 5 m 1 s 5 m

16. Ball dropped: vectors vs. scalars
displacement   distance d d
~ t2 t t
velocity   speed v v
~ t t t
acceleration   acceleration a a
constant t t

17. t (s) d (m) v (m/s) a (m/s2) Ex: ball thrown straight
up with vi = 30 m/s t
(s) d
(m) v
(m/s) a
(m/s2)
-10 30 1
-10 2
-10 3
-10 4
-10 5
-10 6
-10

18. slope = ______________ throughout
v (m/s)
going up 30 20
25 m 10
15 m
5 m
t (s) 1 2 3 4 5 6
-10
-20
-30
slope = ______________ throughout

19. t (s) d (m) v (m/s) a (m/s2) Ex: ball thrown straight
up with vi = 30 m/s t
(s) d
(m) v
(m/s) a
(m/s2)
-10 30 1 25 20
-10 40 10 2
-10 3 45
-10 4
-10 5
-10 6
-10

20. slope = ______________ throughout
v (m/s)
going up
coming
down 30 20
25 m 10
15 m
5 m
5 m
t (s) 1 2 3 4 5 6
15 m
-10
25 m
-20
-30
slope = ______________ throughout

21. t (s) d (m) v (m/s) a (m/s2) Ex: ball thrown straight
up with vi = 30 m/s t
(s) d
(m) v
(m/s) a
(m/s2) 30
-10 1 25 20
-10 40 10 2
-10 3 45
-10 4 40
-10
-10 5 25
-20
-10
-30 6
-10

22. slope = ______________ throughout -10 m/s2
going up
coming
down 10
v (m/s)
t (s) 1 2 3 20
5 m
15 m
25 m 30 4 5 6
-30
-20
-10
positive d
negative d
top
slope = ______________ throughout
-10 m/s2

23. Going Going down: time up: v time 3 s 3 s 5 m 2 s 4 s 15 m 1 s 5 s
3 s
5 m
2 s
-10
4 s 10
15 m 20
-20
1 s
5 s
25 m 30
6 s
0 s
-30
time v

24. At what time is the ball at its highest point? t = 3.0 s
What are the v and a at that time?
v =
a =
-10 m/s2
How do the the last 3 sec of this example compare
to the example of a ball dropped from rest?
the same
What will the graph
of speed vs. time
look like? 30 20 10
t (s) 1 2 3 4 5 6

25. v (m/s)
Ex. How does the picture change if ball
is thrown up a with different initial
speed, say vi = 20 m/s? 30 20 10
t (s) 1 2 3 4 5 6
-10
-20
-30

26. v (m/s)
Ex. What if ball is thrown up with
an initial speed vi = 10 m/s? 30 20 10
t (s) 1 2 3 4 5 6
-10
-20
-30

27. v (m/s)
Ex. What if thrown down a with speed
vi = 10 m/s? 30 20 10
t (s) 1 2 3 4 5 6
-10
-20
-30
Ball continues down until
it strikes the ground.

29. displacement:
velocity:
vf = vi + at
d = vit + ½ at2
With vi = 0 and a = -10
With vi = 0 and a = -10
vf = (-10)t
d = 0t + ½ (-10)t2
vf = -10t
d = -5t2
For t = 0, 1, 2, ….
For t = 0, 1, 2, ….
vf = -10t = -10(0) = 0
d = -5t2 = -5(02) = 0
= -10(1) = -10
= -5(12) = -5
= -10(2) = -20
= -5(22) = -20
= -10(3) = -30
= -5(32) = -45