### Notes:

The Trajectory - Angle 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). This in turn causes the vertical velocity to change by -9.8 m/s each second. As the object moves upward, it slows down and as the object moves downward it speeds up. Meanwhile, the absence of a horizontal force means that the projectile does not accelerate horizontally but maintains a constant horizontal velocity. This Concept Builder supports the internalization of these concepts as students do three different types of things in three different activities. Those actvities include ...

• Activity 1 - Horizontal and Vertical Speed: Students make comparisons and rankings of the horizontal and vertical speed of a projectile for several locations along the trajectory.
• Activity 2 - Vector Diagrams: Students identify the vector diagram for three locations along a projectile's trajectory when given the vector diagram for a fourth location on its trajectory.
• Activity 3: Time, Time, Time: Students associate the values of the horizontal and vertical components of velocity as displayed in a vector diagram to a specific time in seconds.

All three activities fit well together and complement each other. We highly recommend all three. Nonetheless, each of these activities were designed so that they could exist as stand-alone activities. It is not necessary that students do all three activities if pressed for time or if one of the activities is deemed too difficult or even too easy.

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. Teachers 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.

### 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 - Angle 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.