PROJECTile Motion PBL
0 - Entry Event
1 - What Math Tools Are Useful For Projectile Motion?
2 - Finding Firing Solutions I
5 - Meet the Real World - Adjusting for... Everything
6 - Final Firing Attempt, Using Adjusted Firing Solutions (more than one solution attempt required)
Fire water balloons (or other projectiles) at a target (maybe the teacher?) from 100 yards away. Discuss how hard it is to actually hit such a target in the context given on the introduction page. We need more tools!
Standards
HSF.IF.C.7
HSA.CED.A.2
Provide more tools to model and understand quadratic functions, including transformations using this interactive online lesson.
Introduce the idea of parabolic motion with Dan Meyer's basketball shot. Can you predict the outcome of the shot? Use this online interactive lesson to introduce quadratic equations and why they are needed in this context.
Review modeling and anatomy of parabolas using this delightful parabola game - note, some examples will require assistance
Standards
HSA.REI.B.4
Firing solution modeled... now what? Using the quadratic equation.(nice worksheet here)
The beauty of factoring can be applied even more! (nice worksheet here)
What is that algebra stuff good for? Solving single-variable quadratics.
Standards
All previous standards
Plus HSA.SSE.B.3.B
3 - Finding Firing Solutions II
Standards
HSF.TF.B.7
HSG.SRT.C.8
Convert quadratic solution to power and angle. Some trigonometry may be required. Ok, it's definitely required.
FIRE!
4 - First Firing Attempt - Revision,
Accuracy, and More Math Tools
Standards
All previous standards
Create a complete firing solution and analysis (including x and y velocity, initial firing velocity, total horizontal distance (Hd=Hrt), firing angle, equation, and solution of equation). Collaborate, present, and defend.
Fire!
Begin with the Entry Event and move clockwise. 🏁 A more detailed outline including how to assess each standard available here.
Sine and cosine - how to find initial velocity given x and y velocity. Tangent because we'll need it soon too - just trust me okay?
Inverse sine, cosine, tangent - how to find initial angle - so useful!
Axes, units, and two-variable relationships
Find a firing solution equation! Present it to peers! Discover that there is more to do.... How to translate to a physical set of instructions?
Isn't there an easier way? Introducing the Zero Product Property, which allows backwards factoring creation of equations. (nice worksheet here)
Initial velocity is... b! Initial position is... c! Solutions without c are easier! Use a table (teacher generated) to determine what PSI to use for a given initial velocity.
Finding the Y-intercept in a quadratic equation (it's c!).
Practice previous skills and extend -solving quadratics, then practice finding firing solutions given quadratics (inverse trig and trig). (Students generate their own quadratics and have each other solve them and find firing solutions)
Why didn't my firing solution work like I planned? Adjusting for the real world (especially gravity and wind resistance!). Get theoretical horizontal velocity for the previous solution, then compare to actual horizontal velocity - adjust.
A quicker method for intense moments: complete the square.
Debriefing and celebration!
Note - this section is student directed. Teachers do not directly teach these ideas, rather, they present a problem (how do I solve a quadratic) and allow students to research the solution using web, book, other students, or professionals. Practice below is given as students discover solution methods.