Mr. Rogers' AP Physics C: Mechanics (With IB Physics Topics) Objectives Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Kinematics(1) Vector Addition(2) Projectile Motion(3) Newton's Laws(4)

Chapter 4: Projectile Motion

Standards for AP Physics C Newtonian Mechanics: A. Kinematics (vectors, vector algebra, components of vectors, coordinate systems, displacement, velocity, and acceleration) approx 6%  cumulative 18%
2. Motion in two dimensions including projectile motion

E. Circular motion and rotation
1. Uniform circular motion

 Practice Test Study Guide
 Objectives Essential Question:If Bob stands on the edge of the Grand Canyon and throws a penny straight down or throws it horizontally why or why not would it be in freefall? Forms of Freefall Define freefall. In freefall gravity is the only force acting on an object (air resistance is negligible) Define projectile motion. (An object in freefall given a starting velocity.) State the type of curve a projectile will follow when given constant velocity in one dimension and constant acceleration in another. (Parabola) State the name of the path a projectile follows. (Trajectory) State the acceleration in the x and y dimensions for projectile motion. x-dimension accel = 0 always y-dimension accel = 9.8 m/s/s downward on Earth always   State the condition of velocity in both the x and y dimensions. x-dimension velocity = constant always y-dimension velocity = variable always   State the relationship of the velocity & acceleration vectors in the x direction to those in the y direction. INDEPENDENT Homefun (formative/summative assessment): Questions 1, 3, 5, 7, 9, p. 91; Problems 9, 11, 13, 17 Relevance: The understanding of objects in freefall is a key element in many forms sports including sky diving, skate boarding, ski jumping, etc.
 Activities Lesson 1  Key Concepts: Projectile motion as a form of freefall.   Purpose: Model projectile motion assuming no air resistance and constant acceleration in the y-dimension. Interactive Discussion: Objectives 1-5.  Floppy Disk Projectile Demo: If the x and y dimensions are independent then two disks projected horizontally at nearly the same time should strike the floor at nearly the same time even if they have different velocities. (Place a floppy on the edge of a desk and knock it off with two floppies taped together so that all the floppies fly over the edge almost simultaneously.) In Class Problem Solving:   Private Jackson drops a cannon ball when the cannon fires Resources/Materials: 3 floppy disks, two taped together.
 Essential Question: If we ignore air resistance is there any force to produce acceleration in the x-dimension and what does this tell us about x-dimension velocities?
Projectile Motion with Various Launch Angles
Bombs and Baseballs
1. Solve bomber problems.

• Why did the Japanese use a high level horizontal bomber in WWII to sink the USS Arizona?
• Why would horizontal bombers not normally be used against ships in naval battles?
1. Solve artillery (baseball) problems.

2. State the relationship between the range for projectiles launched at complementary angles with the same initial velocity.

• Why would the Confederates use complementary angles to bombard Fort Sumter?

Homefun (formative/summative assessment): Read: Insultingly Stupid Movie Physics

Chapter 8, Hollywood Bombs: How Filmmaker Physics Misses the Boat, pp 117 - 133

Relevance: From throwing stones to modern artillery, the understanding of projectile motion has had a profound influence on history.

 Lesson 2 Key Concept: The x and y components are independent Purpose: Solve projectile motion problems with various launch angles. Video Clip: Show a video clip of the Bombing of USS Arizona, Pearl Harbor  Video Interactive Discussion: Objective 8 & 9. Review mini-lab results. Group Problem Solving: Working in teams of two, calculate the ranges for angles from 10 to 80 degrees in increments of 10 degrees. List the findings in on the white board. Plot the results and state a conclusion.  Resources/Materials: Pearl Harbor  Video
 Essential Question: Does the force of gravity ever flip flop and what does this tell us about the acceleration due to gravity used in projectile motion calculations?
Projectile Motion with Different
Launch and Landing Elevations
1. Solve projectile motion problems for various take off angles when the impact point is above or below the launch point.
• the artillery problem of shooting down a balloon.
• Jackie Chan jumps from roof to roof
• Jackie Chan jumps from roof to balcony

• Robin hood storms the castle.

Some Movies with Projectile motion:

• Speed

• True Lies

• Back to the Future II

Homefun (formative/summative assessment): Read: Insultingly Stupid Movie Physics

Chapter 9, Leaping Logic: Why Moviemakers Say, "How High" When the Director Says Jump, pp 133 - 147

Relevance: Projectile motion is a key element in action movies.

 Lesson 3 Key Concept: Using components to take advantage of the independence of x and y dimensions.   Purpose: Solve projectile motion problems with various launch angles and with starting and ending points at different locations. Interactive Discussion: Objectives. Projectile motion in movies--how it's really done. Why do jumpers need a landing ramp? Why are stunt drivers buckled into special suspension systems? In Class Problem Solving:   See list under objectives
 Essential Question: How has projectile motion helped shape history?
Hitting Targets With Projectiles
in the Real World
1. Describe the equations used to model air resistance force (Fr).

Low speed:  Fr proportional to velocity
High speed:  Fr proportional to (velocity)2
1. Sketch the trajectory of a hypothetical projectile with and without air resistance.

2. Solve projectile motion problems when the target is moving.

• Why would a WWII bomber be difficult for a ship to shoot down?
• Why would dive bombers be more accurate than horizontal bombers?
• What factors would have made the the fatal shot in the Kennedy assassination easy, assuming it was fired by Oswald?

Relevance: Projectile motion can help shed light on whether Kennedy was or was not shot by a lone assassin.

 Lesson 4 Key Concept: To understand projectile motion is to gain a deeper understanding of history including WWII, the American Civil War, the Kennedy assassination etc.   Purpose: Give students an understanding of how complex projectile motion problems can become and on the part solving them has played in history. Interactive Discussion: Objectives.
 (formative/summative assessment) Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion) Title Analysis of motorcycle jump in True Lies Purpose Determine if the bad guy could have survived the motor cycle jump without being injured. Overview The bad guy drives a motorcycle off the top of a sky scraper, flies across a roadway, and lands in a swimming pool on top of a shorter sky scraper. He is uninjured. Data, Calculations Using your observations from the movie: Calculate how far the bad guy falls by measuring the time of the fall and making appropriate assumptions. Estimate the bad guy's horizontal velocity ( assume the motor cycle's max velocity is 0.5 g on top of the building. measure the corresponding time and calculate final x-velocity.) Estimate how far the bad guy travels horizontally during the jump. (Use objects in the movie for the scale or multiply x-velocity times time.). Estimate the bad guy's total velocity on impact. (Convert this to miles per hour.) Questions, Conclusions Is it likely that the bad guy could have walked away uninjured? Resources/Materials: True Lies Video,  stop watches
 Essential Question: What is the single biggest reason to use a computer for modeling projectile motion problems?

Computer Analysis of Projectile Motion

1. Solve Projectile motion problems with a computer simulation (Interactive physics)

Relevance: With complex situations, a computer analysis is often needed to insure accurate results.

 Lesson 5 Key Concept: How Computers are Used for Projectile Motion Problems Purpose: Introduce students to the modeling of complex problems. Interactive Discussion: Objectives. In Class Problem Solving:   See  Mini-Lab below.
 (formative/summative assessment) Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion) Title Analysis of Bus jump in Speed Purpose Determine if the bus could have made the jump under the right circumstances. Overview In the movie a bus is depicted jumping a 50 ft gap in a highway overpass but there is no incline. Data, Calculations Use both interactive physics and pencil& paper calculations to determine if the jump could have been made  under the right conditions without wrecking the bus . Run the simulation both with and without air resistance. Questions, Conclusions What assumptions in the hand calculations would be likely to introduce significant errors. Does inclusion of air resistance in the simulation significantly affect the results? Resources/Materials: Speed video
 Essential Question: Is a circular orbit a form of freefall?
1. State the direction of centripetal acceleration and force.
2. Compare circular to projectile motion.
3. Calculate centripetal acceleration.

ac = v2 / r

1. State why centripetal acceleration is not actually constant.
2. Calculate period (T) of an object in centripetal motion.

T = (2pr) / vT

Homefun (formative/summative assessment): Problems 25, 27, 29

Summative Assessment: Unit Exam objectives 1- 21

Relevance: An understanding of circular motion is basic to an understanding of orbits not to mention space movies.

Lesson 6
Key Concept: Uniform circular motion results in radial or centripetal acceleration.
Purpose: Understand the similarities and differences between circular and projectile motions.

Interactive Discussion: Objective. Define tangential velocity, centripetal acceleration and force.

In Class Problem Solving:

1. Vertical circle

2. Horizontal circle

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It explains all 3 of Newton's laws, the 1st and 2nd laws of thermodynamics, momentum, energy, gravity, circular motion and a host of other topics all through the lens of Hollywood movies using Star Trek and numerous other films.

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