Transcript Document

UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Day 1
Vectors - Graphical Methods
†After
Attendance
(†EQ Sheet & Concept Map)
•
•
•
•
•
•
•
•
Place HW on my desk
†Pickup a new Essential Question Sheet
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
†Pull out your Translational Motion Concept
Map
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
Chapter 3
Kinematics in Two
Dimensions; Vectors
AKA
“The Life of a Pirate”
2-D Kinematics: Vectors
EQ: How is the use of vectors (“the seafarin’
sort”) different than that of scalars (“those
scurvy dogs”)?
Start: Why don’t
pirates ever provide
directions directly
to the buried
treasure?
How is the use of vectors different than that of scalars?
Vizzini vs. The Dread Pirate Roberts
So who paid attention in science class?
QuickTime™ and a
decompressor
are needed to see this picture.
How is the use of vectors different than that of scalars?
Review of Concept Map & Units of Chapter 3
• Vectors and Scalars
• Addition of Vectors – Graphical Methods
• Subtraction of Vectors, and Multiplication of a
Vector by a Scalar
• Adding Vectors by Components
• Projectile Motion
• Solving Problems Involving Projectile Motion
• Projectile Motion Is Parabolic
• Relative Velocity
How is the use of vectors different than that of scalars?
3-1 Vectors and Scalars
A vector has magnitude as
well as direction.
Some vector quantities:
displacement, velocity, force,
momentum
A scalar has only a magnitude.
Some scalar quantities: mass,
time, temperature
How is the use of vectors different than that of scalars?
3-2 Addition of Vectors – Graphical Methods
For vectors in one
dimension, simple
addition and subtraction
are all that is needed.
You do need to be careful
about the signs, as the
figure indicates.
How is the use of vectors different than that of scalars?
3-2 Addition of Vectors – Graphical Methods
If the motion is in two dimensions, the situation is
somewhat more complicated.
Here, the actual travel paths are at right angles to
one another; we can find the displacement by
using the Pythagorean Theorem.
How is the use of vectors different than that of scalars?
3-2 Addition of Vectors – Graphical Methods
Adding the vectors in the opposite order gives the
same result:
How is the use of vectors different than that of scalars?
3-2 Addition of Vectors – Graphical Methods
Even if the vectors are not at right
angles, they can be added graphically by
using the “tail-to-tip” method.
How is the use of vectors different than that of scalars?
3-2 Addition of Vectors – Graphical Methods
The parallelogram method may also be used;
here again the vectors must be “tail-to-tip.”
How is the use of vectors different than that of scalars?
3-3 Subtraction of Vectors, and
Multiplication of a Vector by a Scalar
In order to subtract vectors, we
define the negative of a vector, which
has the same magnitude but points
in the opposite direction.
Then we add the negative vector:
How is the use of vectors different than that of scalars?
3-3 Subtraction of Vectors, and
Multiplication of a Vector by a Scalar
A vector V can be multiplied by a scalar c; the
result is a vector cV that has the same direction
but a magnitude cV. If c is negative, the resultant
vector points in the opposite direction.
How is the use of vectors different than that of scalars?
The Treasure Map
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
Ahoy sprogs,
How are ye doin' on this fine day? Aye, 'tis a fine day . . . fer
findin' loot. Ye see, I 'ave been sailin' th' high seas fer 300 years.
In me head, I've had th' directions t' a loot that I 'ave written down,
but rum 'n time 'ave played tricks on me, 'n I ‘ave forgotten th' order,
'n where I put them in this cabin. Find th' directions, make a map, 'n
find th' location o' th' hidden loot.
But be ye warned sprogs, thar be danger in th’ search for ye loot.
If ye give up and do not use the fine art of f’sics to find ye loot, then ye
grade will walk th’ plank.
-Cap’n Iron John Flint
How is the use of vectors different than that of scalars?
Summary
• Answer the Essential Question.
• Ticket out the Door
– What changes when you have a negative vector?
– What formula must used to find the magnitude of a resultant
vector?
– Explain how changing the order the vectors are added
together affects the resultant vector. Give an example.
• HW (Write down in your Student Planner):
– Treasure Map Lab: Create your map.
Additional Notes/Practice from
Previous Years
• Adding Vectors by Components
Vectors
• Vectors quantities have magnitude and
direction
• Vector quantities can be represented by an
arrow.
• The length of the arrow represents the
magnitude of the vector quantity.
• The direction of the arrow represents the
direction of the vector quantity.
• We usually call these arrows vectors.
Addition of Vectors
• Two or more scalars may be added together to
get a total:
1 kg + 1 kg = 2 kg
• Vectors may be added too, but the rules for
vector addition are different:
1 km east + 1 km north = 1.414 km northeast
• This new vector (1.414 km northeast) is called
the resultant.
Addition of Vectors
• Two vectors can be added in different orders:
– V1 + V2 = V2 + V1 = VR
• Three vectors can be added in different orders:
– V1 + V2 + V3 = V2 + V3 + V1 = V3 + V1 + V2 = VR
• Vector Directions:
– V1 (5, 2)
– V2 (-3, 4)
– V3 (1, -3)
(-3, 4)
V2
(5, 2)
V1
V3
(1, -3)
Addition of Vectors: Graphical
Methods
• There are two ways to add vectors
graphically:
– tail-to-tip method
– parallelogram method
• Example (overhead: graph paper)
Practice: Addition of Vectors
• Using a piece of graph paper, V1, and V2, add the vectors in the
following order using the tail-to-tip method:
– V1 + V2
– V2 + V1
• Using a piece of graph paper, V2, and V3, add the vectors in the
following order using the parallelogram method:
– V2 + V3
– V3 + V2
• Determine the coordinates of the “final” locations.
Check: V1 + V2
V2
V1
Check: V2 + V1
V1
V2
GO: Vector Mathematics
• Addition of Vectors
• Graphical Methods
Subtraction of Vectors
• The negative vector, - V2, has the same
magnitude as vector, V2, but it is in the
opposite direction
– V1 – V2 = V1 + (-V2)
• Example (overhead: graph paper)
Subtraction of Vectors
• Subtraction Practice:
– V1 - V2 + V3
– -V2 + V3 + V1
• Vector Directions:
– V1 (5, 2)
– V2 (-3, 4)
– V3 (1, -3)
Subtraction of Vectors
• Subtraction Practice:
– V1 - V2 + V3
– -V2 + V3 + V1
• Vector Directions:
– V1 (5, 2)
– V2 (-3, 4)
– V3 (1, -3)
Practice: Subtraction of Vectors
• Using a piece of graph paper, V1, and V2, add the vectors in the
following order using the tail-to-tip method:
– -V1 + V2
– V2 - V1
• Using a piece of graph paper, V2, and V3, add the vectors in the
following order using the parallelogram method:
– -V2 + V3
– V3 - V2
• Determine the coordinates of the “final” locations.
Check: -V1 + V2
V2
-V1
Check: V2 - V1
-V1
V2
Multiplying a vector by a scalar
quantity
• Multiplying a vector by a scalar value only
changes the magnitude of vector, not the
direction.
• Example (overhead: graph paper)
Multiplication of Vectors by a
scalar quantity
• Multiplication Practice:
– -2V1 + V2 - V3
• Vector Directions:
– V1 (5, 2)
– V2 (-3, 4)
– V3 (1, -3)
Multiplication of Vectors by a
scalar quantity
• Multiplication Practice:
–
–
–
–
-2V1 + V2 - V3
(-10,-4)+(-3,4)+(-1,3)=(-14, 3)
-10-3-1=-14
-4+4+3=3
• Vector Directions:
– V1 (5, 2)
– V2 (-3, 4)
– V3 (1, -3)
Day 2
Vector Mathematics
†After
Attendance
(†Pirate Hat)
• Place HW on my desk
• †MAKE A PIRATE HAT!!!
• Pickup a sheet of paper, colored pencils, and
scissors.
• DIRECTIONS: (Add to future slide)
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics: Vectors
EQ: How do you separate vectors (the seafarin’
sort) into their components (their peg legs and
crutches)?
Start: If Billy Gruff
walks around the whole
island to find the
seafarin’ vessel and
Iron John Flint just
goes directly there,
who found the ship?
How do we separate vectors into their components?
3-4 Adding Vectors by Components
Any vector can be expressed as the sum
of two other vectors, which are called its
components. Usually the other vectors are
chosen so that they are perpendicular to
each other.
How do we separate vectors into their components?
3-4 Adding Vectors by Components
If the components are
perpendicular, they can be found
using trigonometric functions.
How do we separate vectors into their components?
3-4 Adding Vectors by Components
The components are effectively one-dimensional,
so they can be added arithmetically:
How do we separate vectors into their components?
3-4 Adding Vectors by Components
Adding vectors:
1. Draw a diagram; add the vectors graphically.
2. Choose x and y axes.
3. Resolve each vector into x and y components.
4. Calculate each component using sines and cosines.
5. Add the components in each direction.
6. To find the length and direction of the vector, use:
How do we separate vectors into their components?
The Treasure Map
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
Ahoy sprogs,
How are ye doin' on this fine day? Aye, 'tis a fine day . . . fer
findin' loot. Ye see, I 'ave been sailin' th' high seas fer 300 years.
In me head, I've had th' directions t' a loot that I 'ave written down,
but rum 'n time 'ave played tricks on me, 'n I ‘ave forgotten th' order,
'n where I put them in this cabin. Find th' directions, make a map, 'n
find th' location o' th' hidden loot.
But be ye warned sprogs, thar be danger in th’ search for ye loot.
If ye give up and do not use the fine art of f’sics to find ye loot, then ye
grade will walk th’ plank.
-Cap’n Iron John Flint
How do we separate vectors into their components?
WebAssign/Lab Time
• Work on WebAssign Problems 3.1 - 3.5 or The Treasure Map
Lab
• Final Copy Criteria
–
–
–
–
–
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
• Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
“You can’t argue with the mathematics.”
• A Story about Thomas Teson, the Interactive
Whiteboard Installation and Pythagorean
Theorem.
How do we separate vectors into their components?
Summary
• Answer the Essential Question.
• Ticket out the Door
If v = 7.5 m/s and  = 30° . . .
– What trignometric function is used
to solve for vx?
– What is the value of vx?
What is the moral/highlight of the story?
V
Vy

Vx
• HW (Write down in your Student Planner):
– Treasure Map Lab: Where is the treasure hidden in reference to
your starting position?
– WebAssign Problems 3.1 - 3.5
Additional Notes/Practice from
Previous Years
• Adding Vectors by Components
How do we separate vectors into their components?
3-4 Adding Vectors by Components
• Any vector can be expressed as the sum of two
other vectors called components.
• †It is most useful if one of these components is
vertical (y-direction) and the other is
horizontal (x-direction).
A = Ax + Ay
How do we separate vectors into their components?
3-4 Adding Vectors by Components
• Because a vector with its vertical and
horizontal components forms a right triangle, it
can be analyzed using:
– the Pythagorean theorem:
• V2 = Vx2 + Vy2
• V  Vx2  Vy2

– (Note: the Pythagorean theorem calculates the
magnitude of the vector)
How do we separate vectors into their components?
3-4 Adding Vectors by Components
– the trigonometric functions: SOH - CAH - TOA
• sin  = opposite side/hypotenuse [SOH]
• cos  = adjacent side/hypotenuse [CAH]
• tan  = opposite side/adjacent side: [TOA]
V
Vy

Vx
Day 3
Projectile Motion
After Attendance
•
•
•
•
•
•
Place HW on my desk
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Projectile Motion
EQ: How can the motion of a projectile be
represented and analyzed as two different
motions?
Start: If a cannonball
is fired straight ahead
as another is dropped,
which one hits the
ground first?
How can the motion of a projectile be represented
and analyzed as two different motions?
3-5 Projectile Motion
A projectile is an object
moving in two
dimensions under the
influence of Earth's
gravity; its path is a
parabola.
How can the motion of a projectile be represented
and analyzed as two different motions?
3-5 Projectile Motion
It can be understood by
analyzing the horizontal and
vertical motions separately.
How can the motion of a projectile be represented
and analyzed as two different motions?
3-5 Projectile Motion
The speed in the x-direction
is constant; in the ydirection the object moves
with constant acceleration g.
This photograph shows two balls
that start to fall at the same time.
The one on the right has an initial
speed in the x-direction. It can be
seen that vertical positions of the
two balls are identical at identical
times, while the horizontal
position of the yellow ball
increases linearly.
How can the motion of a projectile be represented
and analyzed as two different motions?
3-5 Projectile Motion
Demonstration:
free-fall and
projectile
motions time
of impact.
How can the motion of a projectile be represented
and analyzed as two different motions?
3-5 Projectile Motion
If an object is launched at an initial angle of θ0
with the horizontal, the analysis is similar except
that the initial velocity has a vertical component.
How can you solve problems involving projectile motion?
3-6 Solving Problems Involving
Projectile Motion
Projectile motion is motion with constant
acceleration in two dimensions, where the
acceleration is g and is down.
How can you solve problems involving projectile motion?
3-6 Solving Problems Involving
Projectile Motion
1. Read the problem carefully, and choose the
object(s) you are going to analyze.
2. Draw a diagram.
3. Choose an origin and a coordinate system.
4. Decide on the time interval; this is the same in
both directions, and includes only the time the
object is moving with constant acceleration g.
5. Examine the x and y motions separately.
How can you solve problems involving projectile motion?
3-6 Solving Problems Involving
Projectile Motion
6. List known and unknown quantities.
Remember that vx never changes, and that
vy = 0 at the highest point.
7. Plan how you will proceed. Use the
appropriate equations; you may have to
combine some of them.
How can you solve problems involving projectile motion?
Projectile Motion Lab
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
• Hit the Target (Demo/Summary Activity)
How can you solve problems involving projectile motion?
WebAssign/Lab Time
• Work on WebAssign Problems 3.6 - 3.12 or the Projectile
Motion Lab
• Final Copy Criteria
–
–
–
–
–
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
• Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
How can the motion of a projectile be represented and analyzed as two different motions?
How can you solve problems involving projectile motion?
Summary
• Answer the Essential Questions.
• Ticket out the Door
– Explain why the projectile and the free-fall ball hit the ground at the
same.
– Why doesn’t velocity change in the forward direction for the
projectile?
• HW (Write down in your Student Planner):
– Projectile Motion Lab (Questions and Conclusions)
– WebAssign Problems 3.6 - 3.12
Day 4
Projectile Motion - Advanced
Super Equation
Maximum Angle Derivation
After Attendance
•
•
•
•
•
•
Place HW on my desk
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Projectile Motion
EQ: How do vectors allow the formulation of the
physical laws independent of a particular
coordinate system?
Start: During battle, Billy
Gruff, located in the mast of
the ship, is looking down the
barrel of a noble seafarer’s
gun aimed at him from
another ship. What should
he do to divert this fate?
(Jump up, jump up, and get
down or do nothing?)
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
In order to demonstrate that
projectile motion is parabolic,
we need to write y as a function
of x. When we do, we find that it
has the form:
This is
indeed the
equation for
a parabola.
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
• v = v0 + at
• x = x0 + v0t + ½ at2
[where a is constant]
[where a is constant]
• x component (horizontal)
vx = v0x + axt
x = x0 +v0xt + ½ axt2
vx2 = v0x2 + 2ax(x – x0)
y component (vertical)
vy = v0y + ayt
y = y0 +v0yt + ½ ayt2
vy2 = v0y2 + 2ay(y – y0)
y = y0 +vyt - ½ at2
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
• The motion of objects when they follow an arced
path.
• Horizontal Motion (ax = 0) Vertical Motion (ay=-g)
vx = v0x
vy = v0y - gt
x = x0 +v0xt
y = y0 +v0yt - ½ gt2
vx2 = v0x2
vy2 = v0y2 - 2g(y – y0)
y = y0 +vyt +½ gt2
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
• For any projectile with initial velocity of v0 at an
angle  (theta) above the (positive) x-axis:
CAH: cos  = v0x/v0 
v0x = v0 cos 
SOH: sin  = v0y/v0 
v0y = v0 sin 
V0
V0y

V0x
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
• Horizontal Motion (ax = 0)
Vertical Motion (ay=-g)
vx = v0 cos 
vy = v0 sin  - gt
x = x0 + (v0 cos t
y = y0 + v0 sin t - ½ gt2
vy2 = (v0 sin )2 - 2g(y – y0)
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
• If we make our initial position the origin (x0 = y0 = 0), then
x  v0 xt  t  x v0 x
and
y  v0 y t  12 gt 2
then
 x  1  x 
y  v0 y 
 2 g

 v0 x 
 v0 x 
2
 v0 y 
 g  2
y
x 2  x

 v0 x 
 2v 0 x 
y  Ax  Bx 2
• Projectile motion is therefore parabolic (yparabola = Ax – Bx2).
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
3-7 Projectile Motion Is Parabolic
The following is a parabolic graph of y(x) = 5/2 x - x2. Notice that
the path resembles the motion of any sport’s projectile.
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion: The Derivation of
SUPER EQUATION
• If we make our initial position the origin (x0 = y0 = 0), then
x  v0 xt  t  x v0 x and y  v0 yt  12 gt 2
 x  1  x 
y  v0 y 
 2 g

 v0 x 
 v0 x 
2
 v0 y 
 g  2
y
x 2  x

 v0 x 
 2v 0 x 
 v0 sin  

 2
g
y
x 2
x
2 

 v cos 
 2v cos  
0
0

 2
g
y  tan x   2
x
2 
 2v 0 cos  
Note #1: y = Ax – Bx2 (where A = tan  and B = g/(2 v02cos 2))
Note #2: A very important trigonometric identity: 2 sin cos = sin(2)
The Death of Billy Gruff (Part I)
(aka. The Monkey in the Tree)
Will Billy die?!?
Not Billy
TO BE CONTINUED . . .
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion: Determination of the
Maximum Range Angle
• The following is the range graph of projectile motion,
x() = cos2tan.
• To calculate the maximum range distance as a function of angle, find the
angle where the slope is zero (aka. take the derivative and set it equal to
zero, dx/d
 Maximum Range
 Slope = 0; dx/d=0
Range
(m)
Maximum
Angle

Angle ()
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion: Determination of the
Maximum Range Angle
• For a level field, y = 0, therefore
• Solve for x

 2
g
y  tan  x   2
x
2 
 2v cos  
0

 2
g
tan  x   2
x
2 
 2v cos  
0
2
2


 2v 20 


v
v
sin

†
2
2
0
0
   2sin cos
x
cos  tan     2 cos 

 g
 g 
cos
 g
sin(2 )
• To calculate the maximum distance as a function of angle, we take the
derivative of both sides with respect to  and set it equal to zero.
dx
 0 and
d

d  2v 20
2
cos

tan

0


d  g

• The derivative of cos 2tan  = 2 cos2- 1
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion: Determination of the
Maximum Range Angle
 2v 20  d
 2v 20 
2
2
cos

tan


2
cos
 1  0
 g  d
 g 




 2v 20 
2
2
2
2

cos


2
cos


1

0

2cos


1
 g  2 cos   1  0

 cos 

1
2
1



cos
 2 2
 Maximum Range
 2 2 
max
 Slope = 0; dx/d=0
Range
(m)
Maximum
Angle

Angle ()
1
2
 45
dx/d=0
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion: Determination of the
Maximum Range Angle
• Graph of height vs. range (with respective angles denoted):
 =60º
Height
(m)
max =45º
 =30º
Range (m)
• Notice that (1) an angle of 45° maximizes the range distance
and (2) the range of 30 ° = the range of 60 °
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Projectile Motion Lab
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
• Hit the Target (Summary Activity)
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
WebAssign/Lab Time
• Work on WebAssign Problems 3.6 - 3.12 or the Projectile
Motion Lab
• Final Copy Criteria
–
–
–
–
–
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
• Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Summary
• Answer the Essential Question.
• Ticket out the Door
– What is the benefit of SUPER equation?
– Will Billy get killed? Explain.
– Since they have the same range, develop/describe a scenario
where an angle of 60 would be necessary to connect with an
intended target.
• HW (Write down in your Student Planner):
– Projectile Motion Lab (Questions and Conclusions)
– WebAssign Problems 3.6 - 3.12
Day 5
Work Day
After Attendance
•
•
•
•
•
•
Place HW on my desk
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Projectile Motion
EQ: How do vectors allow the formulation of the physical
laws independent of a particular coordinate system?
Start: During battle, Billy
Gruff, located in the mast of
the ship, is looking down the
barrel of a noble seafarer’s
gun aimed at him from
another ship. What should
he do to divert this fate?
(Jump up, jump up, and get
down or do nothing?)
How do vectors allow the formulation of the physical laws independent of a particular coordinate system?
When
wefor
last the
left our
hero, BillyConclusion
Gruff, he was in
Now
Exciting
scope of a noble seafarer, aiming to send him on
of “The
Death
of
Billy
Gruff”
on an eternal voyage.
Will Billy die?!?
Not Billy
How do you use vectors to solve problems involving
relative velocity?
Projectile Motion Lab
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
How do you use vectors to solve problems involving relative velocity?
WebAssign/Lab Time
• Work on WebAssign Problems 3.6 - 3.12 or the Projectile
Motion Lab
• Final Copy Criteria
–
–
–
–
–
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
• Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
How do vectors allow the formulation of the physical laws
independent of a particular coordinate system?
Summary
• Answer the Essential Question.
• HW (Write down in your Student Planner):
– Projectile Motion Lab (Questions and Conclusions)
– WebAssign Problems 3.6 - 3.12
Day 6
Relative Velocity
After Attendance
•
•
•
•
•
•
Place HW on my desk
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Relative Velocity
EQ: How do you use vectors to solve problems involving
relative velocity?
Start: During combat,
how should Billy
“Flatback” Gruff
throw his gun/sword
while attempting the
evasive and daring
†DiRTSCuF maneuver?
†Refer the following slide for a description of the DiRTSCuF maneuver.
How do you use vectors to solve problems involving relative velocity?
The DiRTSCuF Maneuver
• Drop lead shot on the ground ahead of you.
• Run towards your enemy and corkscrew dive on
your back
• Throw your gun in the air in front of the enemy (arrr,
their simple minds)
• Slide under his legs
• Catch your gun.
• FIRE!!!!!
The DiRTSCuF Maneuver Demonstration of the via the
Moving BALLISTICS CART!
How do you use vectors to solve problems involving relative velocity?
3-8 Relative Velocity
We already considered relative speed in one
dimension; it is similar in two dimensions
except that we must add and subtract velocities
as vectors.
Each velocity is labeled first with the object, and
second with the reference frame in which it has
this velocity. Therefore, vWS is the velocity of the
water in the shore frame, vBS is the velocity of the
boat in the shore frame, and vBW is the velocity of
the boat in the water frame.
How do you use vectors to solve problems involving relative velocity?
3-8 Relative Velocity
In this case, the relationship between the
three velocities is:
(3-6)
How do you use vectors to solve problems involving
relative velocity?
Projectile Motion Lab
• Work in groups of no more than 4 sprogs.
• Return all supplies to the counter/cart.
How do you use vectors to solve problems involving relative velocity?
WebAssign/Lab Time
• Work on WebAssign Problems 3.13 - 3.16 or the Projectile
Motion Lab
• Final Copy Criteria
–
–
–
–
–
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
• Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
How do you use vectors to solve problems involving relative velocity?
Summary
• Answer the Essential Questions
• HW (Write down in your Student Planner):
– Projectile Motion Lab (Questions and Conclusions)
– WebAssign Problems 3.13 - 3.16
Day 7
Summary/Work Day
After Attendance
•
•
•
•
•
•
Place HW on my desk
Pickup and sign out your computer
Log into www.plutonium-239.com
Select the Warm-Up link
Complete today’s warm-up and submit it
Logout and return the computer to the cart
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Projectile Motion
EQ: How can the motion of a projectile be
represented and analyzed as two different
motions?
Start: How did
pirates destroy ships
on the high seas?
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Summary of 2-D Kinematics
• A quantity with magnitude and direction is a
vector.
• A quantity with magnitude but no direction is
a scalar.
• Vector addition can be done either graphically
or using components.
• The sum is called the resultant vector.
• Projectile motion is the motion of an object
near the Earth’s surface under the influence of
gravity.
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†2-D Kinematic Essential Questions
• How is the use of vectors different than that of scalars?
• How do you separate vectors into their components?
• How do vectors allow the formation of the physical laws
independent of a particular coordinate system?
• How can the motion of a projectile be represented and analyzed as
two different motions?
• How do you use vectors to solve problems involving relative
velocity?
†Answer these before the test.
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†EQ/WebAssign/Lab
Time
•
†Answer the Essential Questions
•
Work on WebAssign Problems 3.1 - 3.22 or Projectile Motion Lab
•
Final Copy Criteria
–
–
–
–
–
•
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Summary
• Ticket out the Door
Write down two questions and their answer for the test tomorrow and
turn it in.
– One conceptual problem
– One mathematical problem
• HW (Write down in your Student Planner):
–
–
–
–
–
Answer the Essential Questions
Treasure Map
Projectile Motion Lab (Questions and Conclusions)
WebAssign Problems 3.1 - 3.22
Web Assign Final Copy
Day 8
Negotiated Work Day
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†After
Attendance (†Work Day)
•
Answer the Essential Questions
•
Work on WebAssign Problems 3.1 - 3.22 or Projectile Motion Lab
•
Final Copy Criteria
–
–
–
–
–
•
Notes about WebAssign:
–
–
•
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
Positive vs. negative answers (Try a negative sign)
Look at the final unit (hours or minutes or seconds)
Complete the Summary Assignment
2-D Kinematics:
Projectile Motion
EQ: How can the motion of a projectile be
represented and analyzed as two different
motions?
Start: How did
pirates destroy ships
on the high seas?
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†2-D Kinematic Essential Questions
• How is the use of vectors different than that of scalars?
• How do you separate vectors into their components?
• How do vectors allow the formation of the physical laws
independent of a particular coordinate system?
• How can the motion of a projectile be represented and analyzed as
two different motions?
• How do you use vectors to solve problems involving relative
velocity?
†Answer these before the test.
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†EQ/WebAssign/Lab
Time
•
†Answer the Essential Questions
•
Work on WebAssign Problems 3.1 - 3.22 or Projectile Motion Lab
•
Final Copy Criteria
–
–
–
–
–
•
State the problem (Ex. Find displacement)
Draw a picture/diagram
Provide a list or table of all given data (Ex. t = 2 s)
Solve the problem symbolically (Ex. v=x/t  x = vt)
Plug in numbers and units to obtain answer.
(Ex. x = (5 m/s)(2 s)= 10 m)
Notes about WebAssign:
– Positive vs. negative answers (Try a negative sign)
– Look at the final unit (hours or minutes or seconds)
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Summary
•
†Ticket
out the Door (†If not completed yesterday)
Write down two questions and their answer for the test tomorrow and
turn it in.
– One conceptual problem
– One mathematical problem
• HW (Write down in your Student Planner):
–
–
–
–
–
Answer the Essential Questions
Treasure Map
Projectile Motion Lab (Questions and Conclusions)
WebAssign Problems 3.1 - 3.22
Web Assign Final Copy
Day 9
Life of a Pirate
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†After
Attendance
Complete the following with 10 minutes
• Make a 10 cm x 10 cm pirate ship (notebook &
carbon paper)
• Label the front of your ship with an “X”
• Pick up and read through “The Life of a Pirate”
Handout
• Move all of the tables out of the back of the
classroom.
Feed Back for Google Docs
• Was anything confusing on google docs?
• Noteworthy Student Responses
2-D Kinematics:
Projectile Motion
EQ: How can the motion of a projectile be
represented and analyzed as two different
motions?
Start: How did
pirates destroy ships
on the high seas?
How did pirates sink ships on the high seas?
Life of a Pirate
Rules:
1. Your ship must be a minimum of 15 cm
x 15 cm square with carbon paper on
top.
2. Your launcher must be positioned
within 10 cm of your ship, but may not
obstruct the other team’s shots.
3. Ships can’t hide behind or beneath
obstructions (i.e. Chairs, table, etc.)
4. Each group will take turns being first
and follow a prescribed order.
5. BEWARE: Hitting an opponent’s
projectile launcher will sink the
opponent’s ship.
6. Failure to follow the rules will result in
disqualification or an attack from the
powers that be (aka. “The God Ball”)
Sequence of Play:
1. You have three minutes to:
a.
b.
c.
2.
After the allotted time, each ship will have 30
seconds to
a.
b.
c.
3.
Set your angle.
Aim your launcher.
Fire your projectile (in order of course).
Ships have up to 2 minutes to
a.
b.
c.
4.
Place your ships in the playing arena.
Measure range to target.
Calculate the angle.
Turn your ship up to 90º and move it up to a
total distance of 1 meter (you cannot move your
ship backwards).
Measure range to target.
Calculate the angle.
Repeat steps 2 and 3 until only one ship
remains or the rules/sequence of play changes.
NOTE: RULES ARE SUBJECT TO CHANGE AS YOUR TEACHER DEEMS NECESSARY OR
AT HIS/HER WHIM.
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Summary
• Put desk back in place.
• HW (Write down in your Student Planner):
–
–
–
–
–
Answer the Essential Questions
Treasure Map
Projectile Motion Lab (Questions and Conclusions)
WebAssign Problems 3.1 - 3.22
Web Assign Final Copy
Day 9: Test
2-D Kinematic Motion
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†After
Attendance
•
Place HW on my desk (in Reverse Alphabetical Order):
WebAssign Final Copy
Essential Questions
Laboratory Assignment(s)
•
Pickup the following:
Chapter 4 Vocabulary Acceleration
Scantron Sheet
•
Fill in the following on the scantron sheet front:
Name: Write your name on it!!
Subject: PIM
Test: 2-D Kin
Date: S10
Period: Block 2
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
†2-D Kinematics Test
• Do not write on Part I (the scantron questions)
• Put your name on Part II and complete it
• Verify any corrections below that have made before submitting
your test.
• Complete the Chapter 4 Vocabulary Acceleration
Test Corrections
• Question
UEQ: How can the motion of an object be described in a measurable and
quantitative way?
Summary
• Ticket out the Door
Turn in the 2-D Kinematics Test
• HW (Write down in your Student Planner):
– Chapter 4 Vocabulary Acceleration