Projectile Motion
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C HAPTER
Chapter 1. Projectile Motion
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Projectile Motion
Key Concept
Descriptive Paragraph
Lesson Objectives The student will: • Draw and interpret graphs involving two-dimensional projectile motion. • Solve for the instantaneous velocity of a projectile. • Predict a projectile’s range.
Lesson Vocabulary Free fall The condition of acceleration which is due only to gravity. An object in free fall is not being held up, pushed, or pulled by anything except its own weight. Though objects moving in air experience some force from air resistance, this is sometimes small enough that it can be ignored and the object is considered to be in free fall. Projectile motion a form of motion where an object (called a projectile) is thrown near the earth’s surface with some horizontal component to its velocity. The projectile moves along a curved path under the action of gravity. The path followed by a projectile is called its trajectory. Projectile motion is motion in two directions. In the vertical direction, the motion is accelerated motion and in the horizontal direction, the motion is constant velocity motion. Instantaneous velocity of a projectile the velocity of an object at one instant during its motion. In the case of a projectile, the instantaneous velocity 1
www.ck12.org vector would be the resultant of a constant velocity horizontal motion and an accelerated velocity vertical motion. Range A projectile launched with specific initial conditions will travel a predictable horizontal displacement before striking the ground. This distance is referred to as the projectile’s range.
Equations • • • • •
v +v
y = ( i 2 f )t x f = (v cos θ)t + xi y f = 12 gt 2 + (v sin θ)t + yi vx = v cos θ vy = v sin θ
Will it hit the hoop?
Complete the Three-Act Task described below by first asking students to predict which basketball will go in the hoop. http://www.101qs.com/1195-will-it-hit-the-hoop Basketball Lab
Divide students into pairs and move to the school basketball court. (Make sure to get the appropriate clearance to use the basketball courts/basketballs and to remind students to bring pencils and notebooks to record their data). Prompt one person to take a free-throw shot. The other person should make a predictive sketch of the following based on their observations: • • • •
A position-time graph for the horizontal motion of the basketball A position-time graph for the vertical motion of the basketball A velocity-time graph for the horizontal motion of the basketball A velocity-time graph for the vertical motion of the basketball
Move students back to the classroom and provide each group with whiteboards and dry erase markers. Students should create a model for projectile motion by including the following on their whiteboards: • A definition of projectile motion (in their own words) • A simple sketch of the following four graphs for a projectile (make sure to label all axes) – – – –
X-T: Position in the X direction as a function of time Y-T: Position in the Y direction as a function of time Vx -T: Velocity in the X direction as a function of time Vy -T: Velocity in the Y direction as a function of time
• A sentence below each graph describing WHY it looks the way it does 2
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Chapter 1. Projectile Motion
(Refer to sample answers). Optional: Students can use the Video Physics App and/or the Graphical Analysis App on their iPhone, iPod Touch, or iPad to do this activity. See the App descriptions in the chapter overview for more information.
Components of Projectile Motion
Provide students with the following information: A basketball is launched 2 meters above the ground with an initial x-component velocity of +6 m/s and a ycomponent velocity of +8 m/s. Prompt students to answer the following questions in pairs: 1. 2. 3. 4.
What is the time the projectile takes to reach the highest position above the ground? What is the projectile’s highest position above the ground? What is the velocity of the projectile at its highest position above the ground? What is the range of the projectile?
(Refer to sample answers).
The Science of Sports
Challenge students to apply what they have learned about projectile motion to a sport of their choice. They can write a brief paragraph, draw an illustration, or even create a voice-over narration of a video clip like those shown below. Here are some links below that describe the projectile motion of various sports: • Science of NHL hockey projectile motion video (5:35) http://www.nbclearn.com/nhl/cuecard/56639 • Science of NFL Football: Projectile Motion Parabolas http://science360.gov/obj/tkn-video/fc729ef0-22ee-4f61-bb2a-b6c07685fb02/science-nfl-football-projectile-motionparabolas
Class Participation Reflection
At the end of class, prompt students to reflect on their class participation by answering the following questions on a piece of paper and turning it in for your review. 1. Rate your participation in today’s class on a scale from 1-10. Explain the reason for your choice. 2. What was the most significant idea you contributed to your group? 3
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Copy and distribute the lesson worksheet in the CK-12 Physics Intermediate Workbook. You can also upload the PDF or provide the worksheet link on your class website. Lesson Quiz
Copy and distribute the lesson quiz using the CK-12 Physics Intermediate Quizzes and Tests link. link.
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