Vectors - Graphical Methods

Vectors - Graphical Methods
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 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 2

Feed Back for Google Docs
Was anything confusing on google docs? Noteworthy Student Responses

Kinematics in Two Dimensions; Vectors
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? 6

Vizzini vs. The Dread Pirate Roberts
How is the use of vectors different than that of scalars? Vizzini vs. The Dread Pirate Roberts So who paid attention in science class?

Review of Concept Map & Units of Chapter 3
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

3-2 Addition of Vectors – Graphical Methods
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.”

3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
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:

3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
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.

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 17

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. 18

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.

1 km east + 1 km north = 1.414 km northeast
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 = 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)

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

Check: V2 + V1

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)

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

Check: V2 - V1

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) =-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) 39

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? 41

3-4 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, 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: Draw a diagram; add the vectors graphically. Choose x and y axes. Resolve each vector into x and y components. Calculate each component using sines and cosines. Add the components in each direction. 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 46

WebAssign/Lab Time Work on WebAssign Problems 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) 47

“You can’t argue with the mathematics.”
A Story about Thomas Teson, the Interactive Whiteboard Installation and Pythagorean Theorem.

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? HW (Write down in your Student Planner): Treasure Map Lab: Where is the treasure hidden in reference to your starting position? WebAssign Problems 49

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 (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]

Day 3 Projectile Motion

After Attendance Place HW on my desk Pickup and sign out your computer
Log into Select the Warm-Up link Complete today’s warm-up and submit it Logout and return the computer to the cart 55

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? 57

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.

3-5 Projectile Motion It can be understood by analyzing the horizontal and vertical motions separately.

3-5 Projectile Motion The speed in the x-direction is constant; in the y-direction 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.

3-5 Projectile Motion Demonstration: free-fall and projectile motions time of impact.

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.

3-6 Solving Problems Involving Projectile Motion
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 Read the problem carefully, and choose the object(s) you are going to analyze. Draw a diagram. Choose an origin and a coordinate system. 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. 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) 66

WebAssign/Lab Time Work on WebAssign Problems 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) 67

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 68

Projectile Motion - Advanced Super Equation Maximum Angle Derivation
Day 4 Projectile Motion - Advanced Super Equation Maximum Angle Derivation

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?) 72

3-7 Projectile Motion Is Parabolic
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 [where a is constant] x = x0 + v0t + ½ at2 [where a is constant] x component (horizontal) y component (vertical) vx = v0x + axt vy = v0y + ayt x = x0 +v0xt + ½ axt2 y = y0 +v0yt + ½ ayt2 vx2 = v0x2 + 2ax(x – x0) 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 

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 and then 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.

Projectile Motion: The Derivation of SUPER EQUATION
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 and 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 . . .

Projectile Motion: Determination of the Maximum Range 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 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  Slope = 0; dx/d=0  Maximum Range 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 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. 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  Slope = 0; dx/d=0  Maximum Range 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 Graph of height vs. range (with respective angles denoted): Notice that (1) an angle of 45° maximizes the range distance and (2) the range of 30 ° = the range of 60 °  =60º Height (m) max =45º  =30º Range (m)

Projectile Motion Lab Work in groups of no more than 4 sprogs.
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) 86

How do vectors allow the formulation of the physical laws independent of a particular coordinate system? WebAssign/Lab Time Work on WebAssign Problems 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) 87

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 88

Day 5 Work Day

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?) 92

Now for the Exciting Conclusion of “The Death of Billy Gruff”
How do vectors allow the formulation of the physical laws independent of a particular coordinate system? When we last left our hero, Billy Gruff, he was in scope of a noble seafarer, aiming to send him on on an eternal voyage. Now for the Exciting Conclusion of “The Death of Billy Gruff” 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. 94

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 96

Day 6 Relative Velocity

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. 100

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!

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.

In this case, the relationship between the three velocities is: (3-6)

Projectile Motion Lab Work in groups of no more than 4 sprogs. Return all supplies to the counter/cart. 104

Summary Answer the Essential Questions HW (Write down in your Student Planner): Projectile Motion Lab (Questions and Conclusions) WebAssign Problems 106

Day 7 Summary/Work Day

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? 110

Summary of 2-D Kinematics
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.

†2-D Kinematic Essential Questions
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.

†EQ/WebAssign/Lab Time
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 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) 113

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 Web Assign Final Copy 114

Day 8 Negotiated Work Day

†After Attendance (†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 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) Complete the Summary Assignment 116

†2-D Kinematic Essential Questions
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.

†EQ/WebAssign/Lab Time
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 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) 119

Summary †Ticket out the Door (†If not completed yesterday)
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 Web Assign Final Copy 120

Day 9 Life of a Pirate

†After Attendance Complete the following with 10 minutes
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. 122

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. Place your ships in the playing arena. b. Measure range to target. c. Calculate the angle. 2. After the allotted time, each ship will have 30 seconds to a. Set your angle. b. Aim your launcher. c. Fire your projectile (in order of course). 3. Ships have up to 2 minutes to a. Turn your ship up to 90º and move it up to a total distance of 1 meter (you cannot move your ship backwards). 4. 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.

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 Web Assign Final Copy 126

Day 9: Test 2-D Kinematic Motion

†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 2 128

†2-D Kinematics Test Test Corrections
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

Summary Ticket out the Door Turn in the 2-D Kinematics Test HW (Write down in your Student Planner): Chapter 4 Vocabulary Acceleration 130

Vectors - Graphical Methods

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Vectors - Graphical Methods

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