Teacher Notes for Vectors and Projectiles


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


Unit Overview

Compared to other units, this unit is designed to be heavier on math and lighter with concepts. Students will use right-angle trigonometry in the early half of the unit. This includes the use of Pythagorean theorem and the sine, cosine, and tangent functions. Around Day 6 or 7 of the 12-day unit, the unit begins a transition towards projectile motion via the concept of a riverboat problem.

We would suggest three primary goals for these 12 days:
  1. To develop skill at adding multiple vectors to determine the resultant vector.
  2. To comprehend the application of kinematic principles and Newton's laws in describing and explaining the motion of a horizontally-launched and an angle-launched projectile.
  3. To combine projectile motion concepts with kinematic equations to predict how far (horizontally) a projectile will travel, how high it will travel (if launched at an angle), and how much time it will be in the air.


Vector Direction Conventions

Unlike our earlier units, this unit will have situations in which a force or a motion does not align with the conventional north-south-east-west axis. We will rely upon a counterclockwise from east convention to describe a vector's direction. While this is not the only convention, it is the most customary convention in science and engineering courses. At various locations on our site, we also describe a vector's direction as the angle that the vector makes with the nearest axes. So, we might describe a vector as having a CCW direction of 120° or we might describe it as having a direction of 30° West of North. 


Target Practice

Not all classroom's are fortunate enough to have a class set of projectile launchers with a reliable launch speed and a means of easily determining a launch angle. If you do have such a set of launchers, then we have a rather thorough collection of Launcher Labs in our Laboratory section. If such equipment is not available, we have three target practice simulations:


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: Up and Down
    This serves as a great introduction to projectile motion. Questions target a student's ability to read, interpret, and interpolate from a graph, to formulate models that are consistent with data, and to translate information from one representation to another representation (e.g, from a diagram to a graph, and vice versa).
  2. Concept Builder: Head-to-Tail Vector Addition
    Students identify the Head-to-Tail vector addition diagram that is consistent with a given vector addition equation.
  3. Physics Interactives: Vector Addition
    Drag a vector onto the canvas. Drag the arrowhead to change its direction. Repeat up to two more times and guess the direction of the resultant. Click/tap a button and the resultant is drawn. This simulation is accompanied by an excellent Student Activity Sheet and a Concept Checker.
  4. Physics Interactives: Trajectory
    You don't have to say "ignore air resistance" any longer with our Trajectory program. Use our Trajectory modeling program to motivate student inquiry. Or turn it into a student project with our Student Exercise (accompanied by a scoring rubric).


Math Difficulties and the Conservation of Time

No teacher really ever saves time. The amount of time that we have with our students is (mostly) the one constant in our profession. How we use the time and to what topics and goals that we proportion the time is variable. For the most part, time follows conservation laws: it is not created nor destroyed but only transferred from one unit to another unit.

When it comes to time, what works for one teacher will not work for another teacher. While we are unable to save time, we can make decisions that allow us to utilize the time we have more efficiently and effectively. For some teachers, that may mean cutting out some content in one unit and transferring that time to another unit. For many teachers, this unit on Vectors and Projectiles may be one where cuts could wisely be made. If your students had great difficulty with the math of earlier units, then you may want to go light on Learning Outcome #4 (Vector Resolution and Vector Components) and eliminate Learning Outcome #5 (Analytic Method of Vector Addition). And additionally, you may wish to skip entirely the Force in Two Dimensions unit. This decision would allow you to transfer approximately 10-12 days to coverage of other topics. This advice is especially helpful to classrooms having great difficulty with the mathematical manipulatives of the first few units.

Finally, projectile motion can be taught in a Conceptual Physics classroom. Projectile motion equations do not necessarily need to be the focus of the study of projectiles. While we find projectile motion to be a great topic for review of kinematic equations and algebraic problem-solving, it is easy to succumb to too much of it. If your students are having difficulty with the mathematics of physics, then projectile motion mathematics does not need to be the hill you die on. You can keep the problems simpler; restrict every horizontally launched projectile problem to the same type: given vox and height, predict where the projectile will land. And restrict every angle-launched projectile problem to the same type: given vo and theta, how much time will the projectile be in the air. 

On a more general note: Our Algebra-Based Physics course places an emphasis on the use of algebraic problem-solving and analysis. If your students are struggling with the mathematics of physics, your strategy may be too feel out ...
  1. ... how to stretch them without overwhelming them,
  2. ... how to implement the use of algebraic problem-solving without having to issue a lot of Cs and Ds to students who understand Physics but can't do the math,
  3. ... how to proportion time and topics so that there is more emphasis on conceptual reasoning, critical thinking, and analysis and less emphasis on algebraic problem-solving,
  4. ... how to lower stress levels when you present and use a new physics equation,
  5. ... how to use physics word problems to make concepts more meaningful.


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)