### Notes:

The Trajectory - Horizontally Launched Projectiles Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

### Teaching Ideas and Suggestions:

Projectile Motion is a common topic in first-year Physics courses. The topic is both conceptual and mathematical. The concepts that are important include the fact that there is a downward force (gravity) that causes a downward acceleration (the acceleration of gravity), and causes the vertical velocity to change by -9.8 m/s each second. Meanwhile, the absence of a horizontal force means that the projectile does not accelerate horizontally but maintains a constant horizontal velocity. This Concept Builder builds off these concepts by adding the numerical representation. Students complete three tasks on every problem. Those tasks include ...

• the selection of a motion diagram with x- and y-velocity vectors (there are seven choices to choose from)
• the calculation of the x- and y-velocity values at 1-second intervals of time
• the calculation of the x- and y-position values at 1-second intervals of time

A convention is used for velocity that assigns a negative value for a downward velocity. These negative signs will have to be included in the table for the y-velocity values. For the position calculations, the initial launch location is the origin or (0, 0) location. Vertical positions located below this point would have negative position values. These will also have to be included in the table.

Each task does not end until the student has accurately completed the task. As such, an un-ending number of tries are allowed. A Health bar is included in the Concept Builder that tracks students' difficulties. This is described in more detail lower on this page. We do not recommend that the Health bar be used for punitive purposes if making an effort to score this activity. The fact is that students are likely to learn at different rates and an individual with a low Health rating might be the very one who learned the most. The Health bar does however provide a method of recognizing student difficulty when the activity is used as an in-class activity. Teachers who scope the room during this activity can quickly find those who are having difficulty. It also provides feedback to students and acts as a deterrent to random guessing. And it also serves a behind-the-scenes role. Completion of the activity is based upon understanding and improvement. There are five problems in the Concept Builder. Each problem is nearly identical with the only difference being in the initial horizontal velocity. The number of misses is tracked and used to determine the end point for the student. Some students will be done after two problems because they demonstrated understanding from the beginning. Other students will be done after three problems because they demonstrated some understanding and showed improvement from one problem to the next. Other students will have to do all five problems. Once a student has been judged to have demonstrated understanding and/or improvement, they are awarded a "Medal" which displays on the Main Screen along with their name. It serves the useful function of validating student completion of the activity when used in the classroom.

This Concept Builder is intended for use in the middle stages of a learning cycle on projectile motion. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in the separate file) in order to judge the appropriateness of it for their classes. We recognize that there are some physics courses that will delve no deeper into the mathematics of a projectile than is done in this Concept Builder. Yet, intensive problem-solving is not the end goal for some courses. Such conceptual-style Physics courses often use -10 m/s/s for the value of gravitational acceleration. This option is provided in the Concept Builder. The -9.8 m/s/s is the other option. Teahcers will have to decide on which value they wish their students to use and inform them in advance.

We believe that the most valuable (and most overlooked) aspect of this concept-building activity (and any of our Concept Builders) is the Help Me! feature. Each of the three tasks is accompanied by a Help page that discusses the details of completing that task. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

### The Health Bar

This Concept Builder includes a green Health bar that is displayed in the right-side panel of the Concept Builder. The Health bar is updated every time that a student checks an answer or set of answers. The calculation of the "Health" is quite complicated and considers several variables. Here's some insights into the calculations of Health:

• Missing an answer on the first task (selecting the proper velocity vector diagram) has twice the impact upon the health as missing a question on the second or third task.
• Having one incorrect value on the second and third tasks has the same impact upon the Health as missing all eight values.
• An incomplete table cell on the second and third tasks is considered a "miss" and will negatively effect the Health. It is thus advantageous for students to complete the entire table before checking the answers.
• Missing a question on the second or third problem has twice the impact upon the Health as missing the same question on the first problem. It is expected that students will demonstrate inprovement from repeating the same problem (same, with the exception of the launch velocity) a second or third time.
• Missing a question on the fourth or fifth problem has three times the impact upon the Health as missing the same question on the first problem.
• The Health can never increase. Progress is demonstrated by the completion of problems, but that does not have any effect upon the Health.

### Related Resources

There are numerous resources at The Physics Classroom website that serve as very complementary supports for this Trajectory Concept Builder. These include:
• Minds On Physics Internet Modules:
The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments VP7, VP8, VP9, and VP10 of the Vectors and Projectiles module provide great complements to this Concept Builder. They are best used in the middle to later stages of the learning cycle. Visit the Minds On Physics Internet Modules.

Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The aforementioned assignments can be found on App #1 of the six-part app series. Visit Minds On Physics the App.

• Physics Interactives: Our Physics Interactives section includes a collection of interactive simulations that help students visualize concepts by interacting and observing the relationships between variables. There are three simulations in the Vectors and Projectiles section of the Physics Interactives that will coordinate with this Concept Builder. The links are provided below. The Projectile Simulator serves as a suitable pre-cursor to this Concept Builder. The Turd the Target activities are good follow-ups for those courses that emphasize the mathematics of projectiles and its use in solving problems. These include the following:

Projectile Simulator

Turd the Target

Turd the Target 2

• Curriculum/Practice: Several Concept Development worksheets at the Curriculum Corner will be very useful in assisting students in cultivating their understanding, most notably ...

Projectile Motion

Visit the Curriculum Corner - Kinematics.

Additional resources and ideas for incorporating Trajectory - Horiontally Launched Projectiles into an instructional unit on Vectors and Projectiles can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.