Teacher Notes for Free Fall and Projectiles

 

Lesson Plans || Learning Outcomes and Activities || Teacher Notes || Labs

 

Unit Overview

It is difficult to think of the topic of free fall and projectiles without thinking of kinematic equations. And for most of us, kinematic equations with a couple of terms on one side of the equation or the other is off-limits for a Conceptual Physics course. And we agree with that assertion. But that does not by necessity reduce a 12-day unit to a 4-day unit. 

Our Conceptual Physics unit on Free Fall and Projectiles is very process oriented. But the processes being emphasized veer far from algebraic manipulation of equations and instead relies upon the use of graphical and numerical displays. Students spend considerable time analyzing data and graphs, creating data and graphs and vector diagrams, and using such representations to answer questions and complete lab challenges.

We would suggest three primary goals for these 12 days:

1. To be able to describe with words, graphs, vector diagrams, and data tables the motion of projectiles moving with an up-and-down motion and with a parabolic motion.
2. To utilize numerical data and graphs to make predictions about how fast (both horizontally and vertically) or how far (both horizontally and vertically) a free-falling projectile will move.
3. To develop an inquisitive question regarding the effect of air resistance upon an air-borne object and to use a numerical modeling program to answer such a question with a claim and supporting evidence and reasoning.

The last of the three goals is a project-based goal that we have written into the unit. Some teachers may opt out of the project. Such a decision would not impact any remaining part of the unit and would simply save a few days for use on another topic.


 

The Mathematical Approach

A common approach to projectile motion is to eventually get around to using kinematic equations to solve projectile problems. We have placed a strong emphasis upon the use of kinematic equations in our on-level Physics course and our Honors Physics course. In our Conceptual Physics course, we would never use the term kinematic equation, nor would we ever use a d = v_o•t + 0.5•a•t² equation (or anything comparable). While students will multiply a horizontal speed by a time to get a horizontal displacement, it is presented as more of a concept associated with the meaning of speed and its application. For instance, an object moving horizontally at 8 m/s for four seconds will travel 8 m each of those 4 seconds; so that's a total horizontal distance of 8 + 8 + 8 + 8; 32 meters. That's more arithmetic than algebra and it's something every high school junior or senior should be able to do whether they are in an on-level or a conceptual-level Physics course. 

In our Conceptual Physics unit on Free Fall and Projectiles, the emphasis is upon looking for patterns in the data associated with distance fallen and time of fall and using a plotting program to generate an equation that fits those numbers. Then students use their equation to make further predictions. A similar approach is taken with speed-time data - finding the patterns associated with the vertical speed and the time and then using those patterns to make predictions. With a value of g of 10 m/s/s, this becomes relatively simple math. 

Another emphasis of the Conceptual Physics course is on using a graph of horizontal and vertical position as a function of time to relate d_x, d_y, and t. We have provided links to several pre-made Desmos graphs that utilize the initial height and the horizontal launch speed as a manipulable variable. A slider or an input field can be used to set these two parameters and thus change the graph that is being analyzed. With this approach, labs can be performed that are similar to those that might be done in an on-level or honors-level Physics course. For instance, there are two different labs in which students use a vertical displacement or a hang time for an upward launch to determine the launch speed of an object. And in the final lab, students perform the traditional hit-the-target challenge that you would find in an on-level or honors-level Physics course. The big difference is that Conceptual Physics students are manipulating graphs instead of manipulating equations. And the task of manipulating and interpreting those graphs requires a whole lot more conceptual understanding of Physics than the task of manipulating the equations. 


 

Our Lesson Plans

As is our practice, we have presented a collection of daily lesson plans as a illustration of how the tools of our course can be put together to form an effective unit of student. We have also organized these tools around a set of learning outcomes. While we have taught this unit with real Conceptual Physics students, we unfortunately do not have the Think Sheets and Lab material in a readily presentable form. They will be eventually gathered together and included in our Conceptual Physics Course Package. Because the mathematical approach that we have taken is so different than anything that we have on our website, we have provided considerably more detail about our Think Sheets. The hope is that there is enough detail to allow teachers to implement the approach with their classes. This course is being prepared in July of 2024. As soon as we complete it, we will be devoted ourselves to two lengthy projects; one of those projects is the creation of the Conceptual Physics Course Package. We will have everything neatly packaged together at that time.

 

Labs

We have proposed four labs for this unit. Since we do not have any Teacher's Guides available, we will supply some notes here:

Lab 1: The first lab requires the use of Video Analysis software. There are several commercial packages available for a small cost. Tracker is a free version that has gained popularity among the Physics teaching community. Students will need to capture video of balls of varying mass rising and falling. The videos can be analyzed to obtain a velocity-time graph. The slope can be acquired to obtain an acceleration. Values of acceleration and mass can be collected from all lab groups. We have found it useful to collect data throughout the day for several classes and to display the data to students the following day.

Lab 2: Lab 2 involves the vertical launch of an object. We have used a Stomp Rocket similar to those found in toy stores. Anything that launches an object upward can be used. If you can't find a launcher then throw a tennis ball vertically upward. Students acquire the time for the object to rise to its peak and return to its launch height. A single trial is needed. They can determine the launch speed (initial speed) and the peak height from this time value. We allow students to use a Desmos graph.

Lab 3: Lab 3 requires a projectile launcher. If you plan on doing Lab 4 as well, then you will need to have a projectile launcher that has some relatively high precision. That is, it consistently launches the projectile at the same speed. We prefer those made available by Pasco Scientific. They can be very pricey, but they are precise and will work well for Lab 4. Students will use the same launcher on Lab 4 that they used on Lab 3. Whatever launchers are used, it is imperative to emphasize the wearing of goggles and attention to lab safety. 

In Lab 3, students launch the projectile vertically. They should be able to stand on a chair or table with a couple of meter sticks or measuring tape stretched out and determine the peak height. Run several trials and determine an average height value. From the peak height above the launch position, students can use the provided Desmos graph to determine the launch speed. The graph is made for high-speed launches. Students can zoom in on the graph to view the trajectory for a low-speed launch. They will need to use a trial-and-error method to determine the launch speed; they can manipulate the launch speed and see what peak height it gives. The continue the trial-and-error process until they have found the launch speed that leads to the measured height. Values for launch speed can be entered into the field on Desmos.

Lab 4: Using the same launcher from Lab 3, students conduct Lab 4 to predict where a target must be placed in order to launch the projectile horizontally into the target. We have provided a Data sheet for Lab 4 on our Lab page. Our practice is to have one projectile for all students. Each lab group gets one shot at the target. Lab groups can set up their launcher, make their measurements, perform their "calculations" (actually, measurements with Desmos graphs), and place their target on the floor where they think the projectile will land. The target can be a sheet of paper with a set of concentric circles (smaller circle for best score) with a sheet of carbon paper placed on top of it. Or for more dramatic results, use a cylinder that stands upright on the floor. If using a cylinder, it is important that students measure d_y as the distance from the launcher vertically down to the top of the cylinder. You know your students better than we do; but we would recommend targets that are large enough to allow for success and to compensate for variability in launch speed. 1-meter diameter cylinders are a bit extreme; but cylinders the size of old-fashioned film canisters is not going to lead to much success. We cut long packaging tubes with ~8-inch diameters into sections and have provided each lab group a cylinder as the target. If you have a single projectile launcher, you can provide cylinders of varying height to different lab groups.

 

Project - Trajectory

We have included an open-ended project in our 12-day unit plan. Those teachers who opt out of the use of the project could shorten the unit by as much as two to three days. The Student Project can be found in the Vectors and Projectiles unit of our Physics Interactives section. Students ask and answer a question of their own choosing using a spreadsheet-like, numerical modeling program titled Trajectory. The project has some structure to it, stepping students through the brainstorming of a question, the generation of a purpose of study, the design of the study, and the execution of the study. Once the study is conducted, students create a short report in which they describe what they did, present the data that they collected, and make a claim that is supported by their evidence and reasoning. 

The numerical modeling program is relatively easy to use. It outputs data in the form of a data table with several columns and in the form of any one of nine possible graphs. Screen captures of the data or the graphs can be taken for insertion into their reports. Our program does the calculations, but students are responsible for the design of the study and the interpretation of the data tables and graphs. In this sense, the project fits well with the flavor of the unit in which data and graphs are used to answer questions. 

We have provided the student activity as both a PDF and a Microsoft Word document. There is a scoring rubric available for those who wish to use it. The downloads can be accessed here.

 

The Calculator Pad

As a teacher of Conceptual Physics, it is unlikely that you are looking for more physics problems to inflict on your students. However we recognize that classrooms exist on a spectrum and there may be some situations in which teachers have opted to use our Conceptual Physics course plan but have students that lie on the spectrum in the region between Conceptual Physics and On-Level Physics. 
If that is the case, you may be interested in the use of kinematic equations to solve projectile motion problems. You will find plenty of these types of problems in the Calculator Pad section of our website. One-dimensional free-fall problems can be found in our Kinematics chapter. And projectile motion problems can be found in our Vectors and Projectiles chapter.

 

Other Resources

There are a few resources that we did not list in our Lesson Plans and Learning Outcomes and Activities that you may find to be very helpful or more in-style with your approach. These include:

1. Science Reasoning Center: Ballistics
   This activity compares and contrasts the trajectories of an airborne object in the absence and in the presence of air resitance. Factors that affect the amount of air resistance are covered. Questions target a student's ability to read a complex graph and to use equations, to use information regarding changes in object shape, area, and mass to predict the characteristics of the resulting trajectory, and to use the relationship between air resistance and object speed.
2. Concept Builder: Trajectory - Angle-Launched Projectiles
   This Concept Builder focuses on the conceptual and numerical nature of the horizontal and vertical velocity vectors of an object that is launched upward at an angle to the ground.
3. Physics Interactives: Projectile Simulator - Angle-Launched Projectiles Activity
   This Student Activity Sheet accompanying our Projectile Simulator provides students with a great activity exploring the concepts and variable relationships associated with angle-launched projectiles. There is an accompanying Concept Checker for this activity.
4. Minds On Physics: Mission VP10 on Displacement and Time for a Projectile
   Students identify and describe the variables which effect the time of flight and the horizontal and vertical displacement of a projectile.

 

 

Teacher Presentation Pack

We will probably say this a lot. But we think it is worth saying. Our Teacher Presentation Pack is a huge time-saver. For early-career and cross-over Physics teachers, it may also become a life saver. It includes a large collection of Slide Decks, animations, and graphics for use in your classroom. Once downloaded, you can modify and customize the Slide Decks as needed. The slides are highly organized and (mostly) graphical; they make great graphic organizers for any student, and especially for the struggling student. 



 

Also Available ...

Physics teachers may find the following for-sale tools to be useful supplements to our Lesson Plan and Pacing Guide section:

 

1. Task Tracker Subscription (annual purchase)
   A subscription allows teachers to set up classes, add students, customize online assignments, view student progress/scores, and export student scores. Task Tracker accounts allow your students to begin assignments in class or at school and to finish them at home. View our Seat and Cost Calculator for pricing details.
    
2. The Solutions Guide
   We publish a free curriculum with >200 ready-to-use Think Sheets for developing physics concepts. The Solutions Guide is a download containing the source documents, PDFs of source documents, and answers/solutions in MS Word and PDF format. An expanded license agreement is included with the purchase. (Cost: $25 download)
    
3. Teacher Presentation Pack
   This is a large collection of downloadable content packed with nearly 190 Microsoft PowerPoint slide decks, the corresponding Lesson Notes (as PDF and fully-modifiable MS Word format), about 170 animations (in .gif, .png, and .mp4 file formats), a countless number of ready-to-use images (including the original source documents that would allow for easy modification of those images), and a license that allows teachers to modify and use all the content with their classes on password-protected sites (such as course management systems).  (Cost: $40 download)
    
4. Question Bank
   We distribute a Question Bank that includes more than 9300 questions neatly organized according to topic. The Question Bank is the perfect tool for busy teachers or new teachers. Even if you don't use the website with your classes, the Question Bank will assist you in quickly putting together quizzes, tests and other documents with high-quality questions that target student's conceptions of physics principles. And if you do use The Physics Classroom website, the Question Bank is the perfect complement to the materials found at the website. (Cost: $25 download)