t

v

vi

Ex. An object moves in ________________ with an ____________________ and an ____________________ .(When graphing v vs. t, the area = _____________ .)

vf

t

The distance if there is no acceleration:

The extra distance due to acceleration:

dA =

dB = = = =

Total distance d: d = dA + dB

d =

If an object is not accelerating, then ___________In this case, the last equation becomes:

d =

This last equation is really the same as:

v =

d =

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:

but:

All of these equations This is called:only describe motion: _____________________

are all in your_____________ .

is _______ in PhysRT

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 rightd = ________ if is moves downward/to left.

Typical physics word problems involve objectsmoving in ____ direction that:

….begin at one point with an_________ speedor velocity:

…. and end at another pointwith a __________speed or velocity:

….and move a distance or displacement ____

with an average speed _____

and at an acceleration _____

during a time interval of _____ .

quantity symbol unitabbrev. of unit

time

distance ordisplacement

speed orvelocity

acceleration

Use units to help you solve problems:

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 thatis 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…

___________from rest:

_______up:fired ______________:

fired up or down _______________:

_________down:

…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 _________________________

Ex 1: A ball is dropped. How far will it fall in 3.5 seconds?

given:

unknown:

equation:

I. ______________ motion

A. Dropped Objects.

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 itsvelocity at the instant it hits ground if it falls for1.3 seconds? given:

unknown:

equation:

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?

Ex. A ball is tossed up with an initial speed of24 meters per second. How high up will it go?

given:

unknown:

equation:

What total distance will it travel before it lands?

What will be its resultant displacement when it lands?

B. Objects Fired Up or Down.

For a ball fired or thrown straight up:

1._______ d each second on way up2.______ 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 longwill he be in the air?

given:

unknown:

equation:

How much time did he spend going up?

Ex. A shot put is thrown straight down froma 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:

Ex: ball dropped from rest

v (m/s)

t (s)

t

(s)

d

(m)

v

(m/s)

a

(m/s2)

0

1

1 2 3

-10

-20

-30

2

3

4

B. Graphical analysis: use a ≈ _____________

-40

total d

0 m

time

0 s

1 s

2 s

3 s

velocity

See any patterns?

Ball dropped: vectors vs. scalars

v

t

v

displacement distanced

velocity speed

acceleration acceleration

d

a a

t

t

t

t

t

t

(s)

d

(m)

v

(m/s)

a

(m/s2)

0

1

2

3

4

Ex: ball thrown straight up with vi = 30 m/s

5

6

0 30

10

v (m/s)

t (s)1 2 3

20

30

4 5 6

-30

-20

-10

slope = ______________ throughout

Going up:

Coming down:

time

0 s

1 s

2 s

3 s

v

v time

6 s

5 s

4 s

3 s

What will the graph of speed vs. timelook like?

At what time is the ball at its highest point?

What are the v and a at that time?

How do the the last 3 sec of this example compareto the example of a ball dropped from rest?

10

t (s)1 2 3

20

30

4 5 6

t =

v = a =

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).

Old way:

_______________method:

A

BA. Adding Vectors.

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

B

Note: R is _____________ ____________ in the old and new methods

point:

Head to tail: Parallelogram:

Ex: Add and

Ex: Add and

Head to tail: 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.

50 m/s

40 m/s speed =

tan =

=

mag:

dir:

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, or2/ use ____________ functions.

Ex: Using a scale.

Measure vx and vy:

vx = _____ cm = ______ m/s

vy = _____ cm = ______ m/s

v = m/s

What is the scale used in the diagramat right?

1 cm = ____ m/s

v

In the Math section of your PhysRT:

A can be_________________,not just velocity v.

Ex: Using trig functions.

Notice also: speed v = ____________ (Pythag. Thm.)tan = __________

= 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.

vx = vcos = = =

vy = vsin = = =

Note:1. Vectors vx + vy = ____ b/c ____________________________

2. The magnitudes 40 + 23 _____________________________

3. (vx2 + vy

2)1/2 = (402 + 232)1/2 = ______ = ________________

Addition:

Head to tail:

Parallelogram:

C. Resolution is the __________________of Addition:

v

Resolution:

gives youcomponents:

Ex. The same vector can be resolved into________________components, depending on how the __________ are chosen.

v

vhas these

______________

…still add up to the ________ v

…that add up to v:

Use the same v, but now _________ the axes:

…butthese new

_____________

This v:

And the axes need not be ___________________ :

…again add upto the ________ v.

…with new _____________

________ v

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 landingis called the ____________________.

horizontal distance traveled = _____________

Ex. Ball 1 is________________. Ball 2 is fired __________________

vi

1 2

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.

The trajectory (path)is a________________.

vi

vi

With no ____________________, only the force of ___________ acts on the object:

Air resistance acts in the direction _____________to its velocity. This __________________ its range.

The trajectory is ________________ a parabola.

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 =____________

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 _______________

3. The initial velocity is purely _________________: viy = ___________ (initially, no y _______________)vi = ________ ("horizontally fired")

velocity: vf = vi +at

vfx =

Horizontal (x) motion: ax =______

displacement: d = vit + ½ at2

dx =

dx =

dx =

vfx =

The x motion is _________________.

dx

t

t

vfx

vfx =

velocity: vf = vi +at

vfy =

Vertical (y) motion: viy = ____ & ay = __________

displace-ment: d = vit + ½ at2

dy =dy =

dy =

vfy =

The y motion is same as for a _________________.

|dy|

t

t

|vfy|

vfy =

Horizontal (x) motion:

•____________ motion

•____________ x-speed

Vertical (y) motion:

•______________motion

• same as for a ball____________________

ax =

dx =

vfx =

dy =

vfy =

ay =

Summary:

Ex. A 68-kg clown is fired from horizontal cannonwith an initial speed of 40. m/s from a heightof 25 m. What is her time of flight?

Given:vix =viy =ay =

ax =dy =

Equation:

Unknown:

40. m/s

25 m

m =

What is her range?

Recalculate the new time of flight and range if she is fired with an initial speed of ____________

Time of flight: range:

What is the x-component of her velocity after 1.5 s?

What is her acceleration after 1.5 s?

Ex. A dart fired horizontally strikes a target adistance of 0.15 m below where it is aimed.

What was its time of flight?

If the target was 9.0 m away from the gun, what was its initial speed?

0.15m

blow gun

ay =

ax =

dy =

viy =

Given:

Equation:

Unknown:

vi

a = horizontal motion -___________

1 s 2 s 3 s 4 s

vertical motion – ______________

combined motion -________________

1 s

2 s

3 s

4 s

vi 1 s 2 s 3 s 4 s

1 s

2 s

3 s

4 s

Look at how the velocity changes:

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 ____________, ______________

The velocity is always __________ the path

vtop ______, atop = ___________

To solve the problem,

vi must be ____________

into its horizontal (vix)

and vertical (viy)

_____________________.vix =__________

vi

viy =

_______

There are _____ simultaneous motions:

For ___ motion, use: _____________________

For ___ motion, use: _____________________

Where: vi = _______________ is the initial speed,

and = __________________ is the angle.

A. The horizontal motion is determined by ___ = _______ . Because there is _______ horizontal force, vix __________________ _____________ x-motion.

dx =dx

t

t

vfxvfx =

displacement:

velocity:

acceleration: ax =

t

ax

B. Vertical motion is determined by ___ = _______ .Because of ____________, the y motion is like a ball thrown _______________ with an initial speed ____ .

dy = dy

t

tvfy

vfy =velocity:

acceleration: ay =

t

ay=

displacement:

=

=

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.

370

vix = vicos

= 75 m/s

viy = visin

=

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 =

ay =vfy =

1st Unknown:

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, thetotal time t = _______ s. You could get this timedirectly if you assume vfy = __________ . Then:

To determine her range, you must assume herx motion is ____________ at vi = ____ = _______ .

Given:

ax =

Unknown: vix =

t =

Notice that the ___________ time is used here!

The trajectory (path)is a________________.

vi

With no ____________________, only the force of ___________ acts on the object:

Air resistance acts in the direction _____________to its velocity. This _____________ its max. height 'and range.

The trajectory is _______________________________

vi

vi

ay =

1 s 2 s 3 s

1 s

2 s

3 s

On way up:

horizontal motion -________________

vertical motion –ball thrown________________combined motion -______________

Ex 2: A graphical example

4 s 5 s 6 s

5 s

4 s

6 s

coming down: The motion is exactly the same as that of a

projectile which is _______________________ :

3 s

3 s

vix 1 s 2 s 3 s

1 s

2 s

3 s

Velocity vectors: going up

viy

resultant velocity found by adding ____ and ____ is _______________ to the parabola is = ________ (NOT = ____ ) at the max. height.

vi

v

4 s 5 s 6 s

5 s

4 s

6 s

3 s

3 s

Velocities coming down:

Notice the ______________ with going up

The effect of changing ___ on the trajectory.Assume all are fired with ________________ vi.

Which results in longest range?

Which results in highest trajectory?

In longest time in air?

Which is a parabola?

As increases, the ___ component of vi increases.Because of this: total time in air ________________ , and

maximum height ______________

________________________ angles have the same range.

compl.

angle

angle with greater….

rangetime of

flight

max.

height

80

60

47

Range as a function of assuming rangefor 450 is 100. Fill in the rest:

25

15 30 45 60 75 90

50

75100

0

ang

le