AP PhysicsMonday 13.10.07Standards: 2a1,2,3 add, subtract, and resolve displacement and velocity vectorsObjective: SWBAT apply basic mathematical operations to the displacement and velocity vectors and represent them graphically.

Agenda1. Warm Up2. Review Falling Objects Lab & collect Analysis3. Collect First 3 AP Problems. & Q&A Sheets4. Hand out Solutions to next 2 AP Problems.5. Adding & Subtracting & Graphing Vectors Notes6. Practice

HomeworkCorrect #2 AP ProblemsPractice adding & subtracting displacement & velocity vectors

Warm UpWhat is A+B, what is B+A, what is A-B, what is B-A?

A

B

AP PhysicsTuesday 13.10.08Standards: 2c1 Students should understand the motion of projectiles in a uniform gravitational field. Objective: SWBAT break displacement vectors in components and graph them.

Agenda1. Warm Up2. Review Vector HW3. Component vectors and

their graphs notes4. More Practice breaking

vectors into components

HomeworkVector Component Worksheet

Warm Up

at 30° N of E

Break the following vector into components.

AP PhysicsWednesday 13.10.09Standards: 2c2 Students should understand the motion of projectiles in a uniform gravitational field.

Objective: SWBAT will master finding resultant vectors and breaking vectors into components.

Agenda1. Warm Up2. Review Component Vector HW3. Projectile Motion Notes3. Practice Analyzing Projectile Motion

HomeworkFinding Resultant Vectors & Resolving Vectors p. 18 1,2,3p.20 1,2,5

Warm Up

at 20° S of E

AP PhysicsThursday 13.10.10Standards: Students should understand the motion of projectiles in a uniform gravitational field.

Objective: SWBAT solve projectile motion problems based on an object falling from a high place. CCS.ELA-Literacy.RST11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11-CCR text complexity band independently and proficiently

Agenda1. Warm Up2. Review HW 3. Projectile Motion Reading4. The Basics of Projectile Motion5. Practice

HomeworkD.24 Projectiles launched horizontally 1,2,3,7,8

Warm UpMr. A is playing a game of pool, he will win the game if he sinks the final shot. If the pocket is 1.6 m away at an angle of 30°, how much horizontal and vertical distance will Mr. A’s shot cover in order to sink the shot?

AP PhysicsFriday 13.10.11Standards: Students should understand the motion of projectiles in a uniform gravitational field. Objective: SWBAT score 80% on the quiz

Agenda1. Warm Up2. Projectile Reading 23. Projectile Motion Sample Problem4. Projectile Motion Problems.

Homeworkp.26,27 #1-6

Warm UpA ball is kicked horizontally out of the back of an airplane at 20m/s. If the airplane is 3000m in the air, how far will the ball travel before it hits the ground?

3 equations of Motion

There are three equations of motion that we use. I will derive 1&3

1.

2.

3.

Though you will not need to derive these, these illustrate a very important practice we undertake in Physics. There are situations where we can combine multiple equations in order solve problems that don’t seem to have a solution.

1 is created by combining a=Δv/Δt & Δv=v-v0

2 can be found by graphing the motion of an accelerating object on a v vs t graph and finding its area. It can be derived using calculus.

3 is created by substituting equation 1 into equation 2

No Δx

No v

No t

How to Use the 3 equations of motion

1. The # 1 rule is to use the givens to decide which equation to use. This equation can’t find an x, so don’t use it if you are given displacement or it is an unknown

This equation can’t find v, so don’t use it if you are given final velocity or it is an unknown.

This equation can’t find t, so don’t use it if you are given t or it is an unknown.

We will call this equation of motion #1

We will call this equation of motion #2

We will call this equation of motion #3

How to use the equations of motion day 2?

2. The # 2 rule is avoid quadratics! If one of your givens is a v0 and your unknown is t then equation 2 is going to be messy.

2b.You can avoid this process by using equation 3 then equation 1. Now try solving the same problem using equation 1 & 3.

2a.Right now try to solve for t using: Δx=10m,Vo=20m/s,a=-9.8m/s2

3. Remember what they are useful for. These equations work within the context of uniformly accelerated motion or constant acceleration. This includes no acceleration

Falling Objects Lab Stations

Station 1: A falling Marble. You will first make the appropriate calculation to predict the time it will take for the marble to fall. Then you will actually time it and find the % error between your calculation and your measurement.

Station 2: What is gravity? By measuring the the time it takes for a golf ball to fall at different heights make a linear graph and find the slope of the graph for an accurate value of g. Find the % error. g=9.807m/s2 use significant figures

Station 3: How does gravity work? Directions: Drop the following objects and time how long it takes them to fall to the ground. Does shape matter? Does size matter? Use what you know about gravity to make sense of what you observe. Once you have collected data write a paragraph explaining the physics of falling objects to the best of your ability. a. How does gravity affect a marble and a golf ball? b. How does gravity affect a piece of paper vs. a book? Can you find a way to make paper and a book fall at the same rate?c. Compare a large cylinder and a small cylinder. Does the orientation of the cylinder affect your result?

Be sure to collect all data in class. You may analyze the data and calculate at home if necessary. Justify all of your conclusions with actual data.

Kinematic Vector Practice

Classwork 3: Resultant Vectors1.2.3.4.5.

Breaking Vectors into Components• x component = horizontal component (left to right)• y component = vertical component (up and down)

• If you have a vector, you have a quantity that has a magnitude (size) and a direction. s is a general way to right length or displacement.

• In order to solve problems involving vectors, we benefit greatly by breaking them into components.

• In 2 dimensional physics the components are x and y• In 3 dimensional physics the components are x, y, and z.• We will use 2 dimensions x and y.

s=4m

θ=30°

Breaking vectors into ComponentsWhen you break vectors into components they are written using the following form:

and are called unit vector. They have a magnitude of 1 and their sole purpose is to denote direction.

means the vector component is in the horizontal direction means the vector component is in the vertical direction.

s=4m

θ=30°

x

y

cos30=x/4m

x=cos30(4m)Î

x=3.46mÎ

sin30=y/4m

y=sin30(4m)Ĵ

y=2mĴ

Adding & Subtracting Displacement Vectors

Lets take a look at the vector relationship that creates Δx: The x0 vector is shown to your right. Then x changes by the amount of Δx

so xo + Δx = x

but xo + Δx = x solved for Δx = x-xo

First show the derivation for Δx on the board. Then clarify…

Adding & Subtracting Displacement Vectors

Lets take a look at the vector relationship that creates Δx: The x0 vector is shown to your right. Then x changes by the amount of Δx

so xo + Δx = x

but xo + Δx = x solved for Δx = x-xo

The same derivation works for the Δv vector.

Resolving Displacement & Velocity Vectors

1. ,30°NW , 45°NW

2. ,30°SW , 10°NW

3. ,30°NE , 60°NE

4. ,20°NE , 40°NE

5. ,10°SW , 70°SE

For each of the following, find the displacement and velocity vectors graphically and then find the

displacement using vector components.

Breaking vectors into Components

1.

2.

3.

4.

5.

6.

7.

8.

30 degrees

45degrees

45degrees

60 degrees

The Basics of Projectile Motion

1. Read the 2 pages in the handout, focusing on the question: “What info/knowledge do they want us to take away from this reading?” 5 min2. Break into table groups, discuss the main points of the paragraph, and come to a consensus on the main idea of the test - 4 min3. Write a concise paragraph together as a group explaining

your conclusions you reached in #2 5 min 4. This will be a lab grade.

Projectile Motion Reading 2Read pages 82 – 83, 5 minutes Focus on: What are differences between the motion of horizontal projections and todays motion at arbitrary angles? What are the points of interest in projectile motion? Finally, What is the central idea that the writer would like you to understand? Discuss the reading in groups and answer the questions, 7 minutes

Extra Credit: Worth 1 HW assignment, Derive the Range Equation on p. 85, but do not copy it from the book. You will need to explain each step you take in words in order to receive extra credit.