Free Fall
Projectile Motion – free fall, but not vertical
Free Fall:
•Used to describe the motion of any object that
freely through a vacuum.
is moving _____________________________
gravity
•the only force acting is ________________
air resistance
•no _____________________
, which is a good
slowly
approximation if object moves ____________
up or down
• motion can be _________________
or in an arc
known as a ____________________
parabola
• the results are independent of ___________
mass
•All of the equations of __________________can
kinematics
used as long as you use:
-9.81 m/s2
a = _______
____________
9.81 m/s2 down
-g = ___________________=
= _____________on
or near Earth’s surface
constant
free fall
for the time the object is in ________________
.
Free fall applies to an object that is…
fired up or
dropped
thrown
_________
___________
at
down
_____
down:
from rest:
an angle
__________:
fired
fired
_______up:
horizontally
______________:
in flight
…only for the time while it is ________________.
In all cases:
1. d is _________________if
the object ends up
positive
above
__________
the point where it started.
2. d is _________________if
the object ends up
negative
below
__________
the point where it started.
up or right
3. v is positive if object is going ________________
down or left
4. v is negative if object is going ________________
always -9.81 m/s2
5. a is _________________________
Vertical
I. ______________
motion
A. Dropped Objects.
Ex 1: A ball is dropped. How far will it fall
in 3.5 seconds?
equation:
given:
a = -9.81
m/s2
d = vit + ½ at2
vi = 0
d = 0t + ½(-9.81)(3.5)2
t = 3.5 s
d = ½(-9.81)(12.25)
unknown: d = ?
d = -60. m
Ex. Harry Potter falls freely 99 meters from rest.
How much time will he be in the air?
given:
a = -9.81 m/s2
equation:
d = vit + ½ at2
vi = 0
-99 = 0t + ½(-9.81)(t)2
d = -99 m
-99 = -4.905t2
unknown:
t= ?
t2 = 20.2
t = 4.5 s
Ex. A dinosaur falls off a cliff. What will be its
velocity at the instant it hits ground if it falls for
1.3 seconds?
equation:
given: a = -9.81 m/s2
vf = vi + at
v =0
i
t= 1.3 s
unknown:
vf = ?
vf = 0 + (-9.81)(1.3)
vf = -13 m/s
A rock that has half the mass of the dinosaur
is dropped at the same time. If it falls for the
same time, what will its final speed be?
same
Which will hit the ground first?
neither
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:
a = -9.81 m/s2
vi = 24 m/s
vi
vf = 0
unknown:
d= ?
equation:
vf2 = vi2 + 2ad
0 = 242 + 2(-9.81)d
-576 = -19.6d
29.4 m = d
What total distance will it travel before it lands?
58.8 m
What will be its resultant displacement
when it lands?
0. m
For a ball fired or thrown straight up:
v=0
vi
going
up
vf
less d each second on way up
1._______
2.______
more d each second on way down
tdown
3. tup = _____________
2tdown
2tup = __________
4. ttotal = _______
0
5. vtop =__________
-9.81 m/s2
6. atop= __________
speeddown
7. speedup = _______________
8.If object falls back to its original
-vi
height, then:
vf=______
coming
down
Ex. Mr. Butchko is fired directly up with an
initial speed of 55 meters per second. How long
will he be in the air?
given:
a = -9.81 m/s2
vi = 55 m/s
vi
vf
equation:
a = Δv/t
a = (vf – vi)/t
vf = -55 m/s
-9.81 = (-55 – 55)/t
unknown:
t = (-110)/-9.81
t= ?
t = 11 s
How much time did he spend going up? t = 5.5 s
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:
a = -9.81 m/s2
vi = -15 m/s
vf = -35 m/s
equation:
vf2 = vi2 + 2ad
(-35)2 = (-15)2 + 2(-9.81)d
1225 - 225 = -19.6d
unknown:
1000 = -19.6d
d= ?
1000/(-19.6) = d
-51 m = d
2
-10
m/s
C. Graphical analysis: use a ≈ _____________
Ex: ball dropped from rest
v (m/s)
t
(s)
1
2
3
t (s)
d
v
a
(m) (m/s) (m/s2)
0
0
0
-10
1
-5
-10
-10
2
-20
-20
-10
3
-45
-30
-10
4
-80
-40
-10
5m
-10
-20
15 m
25 m
35 m
-30
-40
time
total d
0s
0m
1s
5m
velocity
5m
0 m/s
-10 m/s
15 m
2s
20 m
-20 m/s
25 m
3s
45 m
-30 m/s
See any patterns?
Ball dropped:
vectors vs. scalars
displacement   distance
d
t
~ t2
velocity   speed
v
t
~t
d
t
v
t
acceleration   acceleration
a
t
constant
a
t
Stop here
Ex: ball thrown straight
up with vi = 30 m/s
t
(s)
0
d
v
a
(m) (m/s) (m/s2)
0
30
-10
1
-10
2
-10
3
-10
4
-10
5
-10
6
-10
v (m/s)
30
going up
20
25 m
10
15 m
5m
1
2
3
4
5
6
-10
-20
-30
slope = ______________ throughout
t (s)
Ex: ball thrown straight
up with vi = 30 m/s
t
(s)
d
v
a
(m) (m/s) (m/s2)
0
0
30
-10
1
25
20
-10
2
40
10
-10
3
45
0
-10
4
-10
5
-10
6
-10
v (m/s)
30
going up
coming
down
20
10
25 m
15 m
5m
1
-10
2
5m
4
5
3
15 m
6
25 m
-20
-30
slope = ______________ throughout
t (s)
Ex: ball thrown straight
up with vi = 30 m/s
t
(s)
d
v
a
(m) (m/s) (m/s2)
0
0
30
-10
1
25
20
-10
2
40
10
-10
3
45
0
-10
4
40
-10
-10
5
25
-20
-10
6
0
-30
-10
going up
v (m/s)
30
positive d
negative d
20
10
25 m
top
15 m
5m
1
-10
coming
down
2
5m
4
5
3
15 m
6
25 m
-20
-30
-10 m/s2
slope = ______________
throughout
t (s)
Going
down:
Going
up:
3s
2s
0
5m
10
20
v
time
0
3s
4s
-10
15 m
-20
1s
5s
25 m
30
-30
0s
time
v
6s
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
0
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
1 2
3
4 5
6
t (s)
v (m/s)
30
Ex. How does the picture change if ball
is thrown up a with different initial
speed, say vi = 20 m/s?
20
10
1
-10
-20
-30
2
3
4
5
6
t (s)
v (m/s)
30
Ex. What if ball is thrown up with
an initial speed vi = 10 m/s?
20
10
1
-10
-20
-30
2
3
4
5
6
t (s)
v (m/s)
30
Ex. What if thrown down a with speed
vi = 10 m/s?
20
10
1
2
3
4
5
6
-10
-20
-30
Ball continues down until
it strikes the ground.
t (s)
What remains the same in all of these graphs?
acceleration = -9.8 m/s2
Open your 3-ring binder to the
Worksheet Table of Contents.
Record the title of the worksheet:
Free Fall WS
velocity:
vf = vi + at
With vi = 0 and a = -10
displacement:
d = vit + ½ at2
With vi = 0 and a = -10
vf = 0 + (-10)t
d = 0t + ½ (-10)t2
vf = -10t
d = -5t2
For t = 0, 1, 2, ….
vf = -10t = -10(0) = 0
= -10(1) = -10
= -10(2) = -20
= -10(3) = -30
For t = 0, 1, 2, ….
d = -5t2 = -5(02) = 0
= -5(12) = -5
= -5(22) = -20
= -5(32) = -45