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Ex. An object moves in ________________ with an
____________________ and an ____________________ .
(When graphing v vs. t, the area = _____________ .)
vf
The extra distance
due to acceleration:
dB =
=
=
=
v
vi
The distance if there
is no acceleration:
dA =
t
t
Total distance d:
d
= d A + dB
d
=
If an object is not accelerating, then ___________
In this case, the last equation becomes:
d
=
d
=
This last equation is really the same as:
v=
after it is solved for:
since v is ______________ when a = 0,
then ______will be the same as _______.
One more equation:
and these equations we studied before:
are all in your
_____________ .
but:
is _______ in PhysRT
All of these equations
This is called:
only describe motion:  _____________________
In these equations, all of the quantities are
______________ . This means they have
_______________ and _______________ .
Ex: If a ball is thrown with an initial speed
of 7 m/s, use:
vi = ________ if is thrown upward/to right
vi = ________ if is thrown downward/to left.
Ex. If a rocket moves a distance of 35 m, use:
d = ________ if is moves upward/to right
d = ________ if is moves downward/to left.
Typical physics word problems involve objects
moving in ____ direction that:
….begin at one
point with an
_________ speed
or velocity:
…. and end at
another point
with a __________
speed or velocity:
….and move a distance or displacement ____
with an average speed _____
and at an acceleration _____
during a time interval of _____ .
Use units to help you solve problems:
quantity
time
distance or
displacement
speed or
velocity
acceleration
symbol
unit
abbrev.
of unit
Word clues:
1. starts at rest  ______________
2. comes to rest  _______________
3. uniform motion  __________ , and
_____________________
4. constant velocity  _________________________
5. constant speed in 1 direction  ___________
6. Acceleration will always be ________________ .
It may be _________________, _________________
or _____ (still constant, but then _____________).
7. slows down: a and v are in _______________
directions
8. If an object collides with another object
(like Earth), then its final speed is _________ !
In this case, "final speed" means the speed
___________________________ it hits.
9. Whatever direction an object is moving is the
direction of its _____________________ .
10. If an object changes direction, then, at that
instant, only its ___________________________
MUST be zero.
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 ________________ .
Free fall applies to an object that is…
fired up or
_________
___________
down _____
down:
from rest:
__________:
fired
_______up:
______________:
…only for the time while it is ________________.
In all cases:
1. d is _________________if the object ends up
__________ the point where it started.
2. d is _________________if the object ends up
__________ the point where it started.
3. v is positive if object is going ________________
4. v is negative if object is going ________________
5. a is _________________________
I. ______________ motion
A. Dropped Objects.
Ex 1: A ball is dropped. How far will it fall
in 3.5 seconds?
given:
unknown:
equation:
Ex. Harry Potter falls freely 99 meters from rest.
How much time will he be in the air?
given:
unknown:
equation:
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:
unknown:
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?
Which will hit the ground first?
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?
given:
equation:
unknown:
What total distance will it travel before it lands?
What will be its resultant displacement
when it lands?
For a ball fired or thrown straight up:
1._______ d each second on way up
2.______ d each second on way down
3. tup = _____________
4. ttotal = _______ = __________
5. vtop =__________
6. atop= __________
7. speedup = _______________
8.If object falls back to its original
height, then:
vf =______
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:
equation:
unknown:
How much time did he spend going up?
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:
unknown:
equation:
B. Graphical analysis: use a ≈ _____________
Ex: ball dropped from rest
v (m/s)
t
(s)
1
-10
-20
2
3
t (s)
0
1
2
3
-30
4
-40
d
v
a
(m) (m/s) (m/s2)
time
0s
total d
0m
1s
2s
3s
See any patterns?
velocity
Ball dropped:
vectors vs. scalars
displacement   distance
d
d
t
velocity   speed
v
t
v
t
t
acceleration   acceleration
a
t
a
t
Ex: ball thrown
straight up with
vi = 30 m/s
t
(s)
0
1
2
3
4
5
6
d
v
a
(m) (m/s) (m/s2)
0
30
v (m/s)
30
20
10
1
2
3
4
5
6
-10
-20
-30
slope = ______________ throughout
t (s)
Coming
down:
Going
up:
v
time
3s
3s
2s
4s
1s
5s
6s
0s
time
v
At what time is the ball at its highest point?
t=
What are the v and a at that time?
v=
a=
How do the the last 3 sec of this example compare
to the example of a ball dropped from rest?
What will the graph
of speed vs. time
look like?
30
20
10
1 2
3
4 5
6
t (s)
II. Understanding Velocity in _________________ .
When an object is moving ____________________
as well as _____________________ , its velocity
has ______ and ______ components ( __________).
In this section, you will study A/ a new way to
______ vectors, and B/ how a velocity vector can
be _________________ (broken up into parts).
A.
Adding Vectors.
B
Old way:
_______________method:
A
New way: _____________________ method:
•draw the 2 vectors as if they come from a
___________________ (see below).
•draw a _____________________ using the 2
vectors as sides
•The resultant R is the _____________________
drawn from the point
A
point:
B
Note: R is _____________
____________ in the old and new methods
Ex:
Add
and
Head to tail:
Ex: Add
Head to tail:
Parallelogram:
and
Parallelogram:
Ex: A train is moving at 50. m/s west. A cannon
on the train is fired straight up with an initial
speed of 40. m/s. Determine the resultant
velocity with respect to someone on the ground.
 Use the ____________________ method.
mag:
speed =
40 m/s
dir:
tanq =
50 m/s
q=
B. Resolving vectors: Any vector can be
_________________ (broken down) into
______________________ (parts)
Steps (after drawing the vector itself):
1. Draw ________________ from the tail end of
the vector. This is often done for you.
1. Draw __________________from the head of the
vector that are _______________to each of the axes
3. Draw the ___________________vectors along the
axes, starting at the axes _______________ and
ending at the ______________________.
v
Ex: The components vx and
vy are also _____________ .
If they are added back
together, you will get
the___________________ .
To determine components, you can either:
1/ set up a scale and _______________directly, or
2/ use ____________ functions.
Ex: Using a scale.
What is the scale
used in the diagram
at right?
1 cm = ____ m/s
Measure vx and vy:
vx = _____ cm = ______ m/s
vy = _____ cm = ______ m/s
v=
m/s
Ex: Using trig
functions.
v
In the Math section of your PhysRT:
A can be_________________,
not just velocity v.
Notice also:
speed v = ____________ (Pythag. Thm.)
tan q = __________
q = tan-1 (__________)
Ex: A ball is launched into the air with an initial speed
of 46 m/s at an angle of 300 to the horizontal. Find the
x- and y- components of the initial velocity.
vy = vsinq
=
=
=
vx = vcosq
=
=
=
Note:
1. Vectors vx + vy = ____ b/c ____________________________
2. The magnitudes 40 + 23 _____________________________
3. (vx2 + vy2)1/2 = (402 + 232)1/2 = ______ = ________________
C.
Resolution is the __________________of Addition:
Addition:
Resolution:
v
Head to tail:
Parallelogram:
gives you
components:
Ex. The same vector can be resolved into________________
components, depending on how the __________ are chosen.
This v:
v
has these
______________
Use the same v, but
now _________ the axes:
…that add
up to v:
…still add up to
the ________ v
v
…but
these new
_____________
And the axes need not be ___________________ :
________
v
…again add up
to the ________ v.
…with new
_____________
Any vector can be resolved into an
________________ number of component pairs.
III. _______________________Fired Projectile:
A projectile (object) is launched horizontally
with an __________________ from a height ______ .
Assume no_____________________.
The time in the air before landing
is called the ____________________.
horizontal distance traveled = _____________
Ex. Ball 1 is________________.
Ball 2 is fired __________________
1 2
vi
Both reach the ground ______________________ ,
regardless of 2's __________________ or ________.
The y motion is ______________ of the x motion.
Remember:
The time it takes a ______________ fired projectile
to fall is ______________ the time it takes a
______________ ball to fall from the same height.
With no ____________________, only the force of
___________ acts on the object:
vi
The trajectory (path)
is a________________.
Air resistance acts in the direction _____________
to its velocity. This __________________ its range.
vi
The trajectory is _____
___________ a parabola.
1.Since the object moves in 2 dimensions, each
d, v and a must be replaced by their components:
For x motion: d, v, a  _______________
For y motion:
d, v, a  _______________
2. No air resistance  only ____________ ,
which is _______________ , in the ____ direction.
There is no _________________ force. Because
of this, the only acceleration a is purely vertical:
ay = ___________
ax =____________
3. The initial velocity is purely _________________:
viy = ___________ (initially, no y _______________)
vi = ________
("horizontally fired")
Horizontal (x) motion:
ax =______
displacement: d = v t + ½ at2
i
dx =
dx
dx =
dx =
velocity:
vf = vi +at
vfx =
vfx =
t
vfx
vfx =
The x motion is _________________.
t
Vertical (y) motion:
viy = ____ & ay = __________
displace2
d
=
v
t
+
½
at
i
ment:
dy =
dy =
|dy|
dy =
velocity:
vf = vi +at
vfy =
vfy =
vfy =
t
|vfy|
t
The y motion is same as for a _________________.
Summary:
Horizontal (x) motion: Vertical (y) motion:
•____________ motion
•______________motion
•____________ x-speed
• same as for a ball
____________________
dx =
dy =
vfx =
vfy =
ax =
ay =
Ex. A 68-kg clown is fired from horizontal cannon
with an initial speed of 40. m/s from a height
of 25 m. What is her time of flight?
40. m/s
25 m
Given:
m=
vix =
viy =
ay =
ax =
dy =
Unknown:
Equation:
What is her range?
What is the x-component of her velocity after 1.5 s?
What is her acceleration after 1.5 s?
Recalculate the new time of flight and range if
she is fired with an initial speed of ____________
Time of flight:
range:
Ex. A dart fired horizontally strikes a target a
distance of 0.15 m below where it is aimed.
0.15
m
blow gun
What was its time of flight?
viy =
ay =
Given:
ax =
Equation:
dy =
Unknown:
If the target was 9.0 m away from the gun,
what was its initial speed?
horizontal motion -___________
vertical motion – ______________
a=
combined motion -________________
vi
1s
2s
3s
4s
1s
2s
3s
4s
Look at how the velocity changes:
vi
1s
2s
3s
4s
1s
2s
3s
4s
The x-component of v is ________________
The y-component of v __________________
Resultant velocity  magnitude (speed) ______________
___________________to trajectory
IV.Projectile fired __________________________
with an initial _________________
Assume no _________________. The only force
acting on the projectile is _________ . This means
the acceleration is ____________, ______________
vtop ______, atop = ___________
The velocity
is always
__________
the path
To solve the problem,
vi must be ____________
into its horizontal (vix)
vi
viy =
_______
and vertical (viy)
_____________________.
q
vix =__________
Where: vi = _______________ is the initial speed,
and q = __________________ is the angle.
There are _____ simultaneous motions:
For ___ motion, use: _____________________
For ___ motion, use: _____________________
A. The horizontal motion is determined by ___ =
_______ . Because there is _______ horizontal force,
vix __________________  _____________ x-motion.
acceleration:
ax =
ax
t
velocity:
vfx =
vfx
t
displacement:
dx =
dx
t
B. Vertical motion is determined by ___ = _______ .
Because of ____________, the y motion is like a ball
thrown _______________ with an initial speed ____ .
acceleration: ay =
=
velocity:
ay
t
vfy =
=
vfy
t
displacement:
dy =
=
dy
t
Ex 1: Ms. Rudd is fired out of a cannon at a speed
of 75 m/s and at an angle of 370 to the horizontal.
75 m/s
370
vix = vicosq
=
viy = visinq
=
To determine how high up she goes and how long
she is in the air, "pretend" she is fired __________
___ but with an initial speed = _____ = __________
Given: viy =
1st Unknown:
ay =
vfy =
2nd Unknown:
How far up?
How long is she in the air?
Because we chose vfy = ___ , this t represents the
time to _________________ . To get the total time
of flight, we must _____________________ . So, the
total time t = _______ s. You could get this time
directly if you assume vfy = __________ . Then:
To determine her range, you must assume her
x motion is ____________ at vi = ____ = _______ .
Given: vix =
Unknown:
ax =
t=
Notice that the ___________ time is used here!
With no ____________________, only the force of
___________ acts on the object:
vi
The
trajectory (path)
is a________________.
Air resistance acts in the direction _____________
to its velocity. This _____________ its max. height '
and range.
The trajectory is _______
________________________
vi
Ex 2: A graphical example
On
way
up:
horizontal motion -________________
vertical motion –ball thrown________________
combined motion -______________
3s
2s
ay =
1s
vi
1s
2s
3s
coming down:
The motion is exactly the same as that of a
projectile which is _______________________ :
3s
4s
5s
6s
3s
4s
5s
6s
Velocity vectors: going up
3s
2s
1s
vi
viy
vix
1s
2s
3s
resultant velocity  found by adding ____ and ____
 is _______________ to the parabola
 is = ________ (NOT = ____ ) at the max. height.
Velocities coming down:
3s v
4s
5s
6s
3s
4s
5s
6s
Notice the ______________ with going up
The effect of changing ___ on the trajectory.
Assume all are fired with ________________ vi.
Which q results in longest range?
Which results in highest trajectory?
In longest time in air?
Which is a parabola?
As q increases, the ___ component of vi increases.
Because of this: total time in air ________________ , and
maximum height ______________
angle
________________________ angles have the same range.
compl.
angle
angle with greater….
range
time of
flight
max.
height
80
60
47
Range as a function
of q, assuming range
for 450 is 100.
Fill in the rest:
100
75
50
25
0
15 30 45
60 75 90
q
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