# Exploring Projectile Motion

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## Objective

Students analyze the velocity components of a projectile to discover that the horizontal component does not change and that the vertical component changes at 9.8 m/s^2.

#### Big Idea

Complicated situations of motion, such as projectiles, can be analyzed using component vectors.

## Context and Supplies

Breaking vectors into components is a theme in 2-D motion and it continues with projectile motion. For this reason, I have decided to make make projectile motion a part of studying two-dimensional forces. In this lesson, students begin to explore projectile motion and the variables involved in determining the path of a projectile. Computers and access to the internet are required to conduct this activity.

There are two goals for this activity. Students use a computer simulation to determine how different variables, such as launch angle and launch speed, influence the horizontal displacement of a projectile. The NGSS performance standard is  Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. Also applicable is HS-ETS1-4 in which students use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem. Students also apply Science Practice 1, asking questions, as they conduct their investigation. The second goal is for students to examine how the horizontal and vertical velocity components of a projectile behave which has students applying Science Practice 4, analyzing and interpreting data, and CCSS Math Practice 2, reason abstractly and quantitatively.

I have the students do a guided inquiry activity on this introduction to projectile motion. In an inquiry activity, students ask their own questions and conduct an investigation. However, there is a structure and goal involved which is what makes it guided. I use this guided inquiry because it gives students some control over the decisions they make and involves them as they build an understanding of the variables that impact a projectiles path.

## Guided inquiry on projectile motion

25 minutes

Students use a computer simulation to determine how different variables, such as launch angle and launch speed, influence the horizontal displacement of a projectile. I instruct students to work in groups of 3-4; each group gets one computer and goes to Walter Fendt's projectile motion Java program. This video gives a quick overview of the simulation and the settings that work best for the students' data collection.

Students are free to choose their own groups which tends to make the groups homogeneous. The purpose of this group learning activity is to get all students to engage in the decision making and observations which is best done with peers who have similar abilities. To ensure that each student is a part of the process, each student gets a Projectile guided inquiry sheet; they have 25 minutes to complete.

Students collect their data right on the handout sheet. They indicate what variables they want to test and report its influence on the displacement of the projectile. It is very important that students set the initial launch height to zero; the goal is to focus on the role of launch angle and speed for this activity. I find that this is harder to do if students are also changing the launch height.

## Direct Instruction on Formulas

10 minutes

Once students complete their guided inquiry sheets, I get their attention as a class and we review students findings. I call on random students to share what variables influence the horizontal displacement of a projectile. Students share that the angle and launch velocity impact how far the projectile goes. Then we move onto the behavior of the x and y velocity components. It is essential that all students see this as we review it, so I display the Walter Fendt's projectile motion Java program as we discuss this. Students see that the horizontal component of the projectile does not change and the vertical component changes at a constant rate.

Then I display the solutions to the back of  the inquiry sheet. In completing this sheet, it is my hope that students recognize that the horizontal component of the velocity vector does not change and that the vertical component of the velocity vector changes at a rate of 9.81 m/s^2. I explain that the beauty and power of physics is that we can take complicated situations, break those problems into parts, analyze those parts individually, and then put the problem all back together to find the solution. The rate at which the projectile changes its velocity is NOT constant! Because of this, we cannot use the constant velocity equations to make predictions about the actual velocity and displacement of a projectile. In order to use those equations, we have to break the velocity into component parts.

I display the Projectile Intro Power Point and ask students to write the projectile motion equations in their notebooks. I give the students a minute to discuss with their groups what they observe about these equations. I then call on the groups to share out their observations and make sure that the following observations are included:

• These are the kinematic equations with new variables that apply specifically to projectile motion
• Instead of "a", we use "g", which is 9.81 m/s^2
• Convention is up is the positive direction and down is the negative direction (though we can change that if we wanted to)
• Vx is constant velocity
• Vy is constant acceleration

This information sets the foundation to be able to solve projectile motion problems, so it is important that all students have this information and that they understand it. The last activity serves this purpose.

## "Choose that Point" Activity

15 minutes

It is important to close the lesson with a summary of what students have learned. This activity helps fortify student understanding of how the velocity components behave on a projectile. I hand out the Choose that Point worksheet so that students analyze the velocity components at various stages of a projectiles path.

Students must think about the values of the components at different parts of a projectiles path. This understanding is essential to the next step of solving projectile motion problems using math, which we do in the next class. I do not collect this sheet, but let students correct their own as I display the Choose that Point Solutions on my document camera at the end of class. We clarify any student misunderstanding through the discussion of the presented solutions.