You are a game designer for Rovio Entertainment, the company that makes Angry Birds. The human resources department wants your input. They are hiring several programmers to build the physics engine for Rovio’s newest game. Here are the demo videos from the top four applicants. Which applicant(s) would you recommend for hire?
These videos were not created by me. I found them online several years ago, but I can’t remember where. If anyone knows, please tell me so I can give the creator proper credit. Thanks!
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Stage 0
“So, as you can see by this free body diagram, gravity is the only force on the ball. Therefore, the ball will move with constant velocity forward while accelerating downward at 9.8 m/s2. Any questions? Great!”
I’m no genius when it comes to this teaching thing. It took me 12 years to get from Stage 0 to Stage 4 for this lesson. And I still have plenty of lessons stuck in Stage 0 and Stage 1!
This video (taken from the Win/Fail Physics collection) is the beginning and the end of a mini learning cycle during my projectile motion unit. At the beginning of the unit, it’s the hook. At the end of the unit, it’s the assessment.
Creating a need to know
By the end of their first viewing, all of my students are yelling “That’s fake! No way!”
“Where’s your evidence?” I ask. “Convince me.”
And students come up with all kinds of weak excuses like “It just LOOKS fake!” or “No one could do that!”
“No,” I say. “Convince me with physics. Justify your claim with scientific evidence.”
(*crickets chirping*)
The kids now have a need to know. They want to know if the video is real or not, but they lack the tools and knowledge to support or refute their original claim. They are now willing to go down the rabbit hole with you.
Whenever possible, I frame my lessons around the Karplus learning cycle: Exploration, Invention, and Application. (It’s nothing special. In fact, most other learning cycles like 5E, 7E, and Modeling are strikingly similar.) Instead of relying on lectures and textbooks, I use the learning cycle so students can construct the conceptual and mathematical models themselves, all within an interactive learning community. By this point in the year, my students have been through several cycles, including constant velocity motion, accelerated motion (including vertical free-fall motion), and balanced/unbalanced forces.
Exploration Phase
Our goal as a class is to develop a model for Kobe’s motion through the air. After some Socratic discussion, we conclude that Kobe’s motion, if real, could be similar to tossed ball. After all, both Kobe and the tossed ball only experience the downward pull of the Earth while in the air. Both Kobe and the ball move vertically and horizontally at the same time. However, as my Force Concept Inventory (FCI) results indicate, many of my students do not grasp the independence of horizontal and vertical motion. So I ask them to forget about Kobe for a minute, and we do two exploration activites:
Pirate Treasure Hunt: Each group gets 10 directions (e.g., “Walk 44 tiles north”). What they don’t know is that all the groups have the same 10 directions arranged in different orders. However, if they follow the steps in order, they will be walking through walls and out windows. Eventually, students realize they can combine all the north-south directions and all the east-west directions and simply walk X paces west and Y paces north. The follow-up class discussion about “Why did you do that?” really gets at the independence of horizontal and vertical motion.
Dropping/Shooting a Bullet: Student use ice cream cone shooter toys to answer the question: “When released at the same time, which hits the ground first: a horizontally shot bullet or a bullet dropped from the same height?” Predictions and justifications must be made. Some students see the connection right away. Others don’t, but the results make for great discussion afterwards.
Which hits the ground first?
Invention Phase
Now we know that horizontal and vertical motion are independent. But we need to create (invent) a more detailed model to describe the motion of a tossed ball. But how will we get the horizontal and vertical motion data in order to create the model? Through Socratic discussion, student decide that trying to mark the position of the ball in the air as it moves won’t work. Nor will using motion detectors. Students decide to use our Flipcams to video themselves tossing the balls and then do a video analysis of the motion in Logger Pro. (Students had done video analysis earlier in the year.) But there are still more questions:
“Wouldn’t the motion depend on how fast the ball is tossed?”
“Wouldn’t the motion of a tall/skinny arc be different than a low/wide arc?”
“Wouldn’t the mass of the ball affect the motion?”
So, as a class, we decide to split up the data collection. One group will vary ball mass, another toss speed, and another arc shape. We’ll share the position vs. time and velocity vs. time graphs created and look for patterns in their shapes and in their equations. This is whole class inquiry — groups are doing different experiments and everyone’s data is needed. Everyone makes a contribution to our classroom scientific community.
Video analysis in Logger Pro (image credit: vernier.com)
After the data collection and analysis, students “whiteboard” their graphs and we have a “board meeting” where each group presents their results and then as a class we try to make connections among the groups and come to a consensus. At the end of the board meeting, the class has created a model for projectile motion: In the horizontal direction…
All position vs. time graphs are straight lines. The slope of the line represents the horizontal speed, which remains constant during flight. This is like our previous model of constant velocity motion.
All velocity vs. time graphs are flat lines. This means the horizontal acceleration is zero which matches up the horizontal position vs. time graph. Again, this is like our previous model of constant velocity motion.
In the vertical direction…
All position vs. time graphs are in the shape of upside-down parabolas, with the time-squared coefficient being about 5 m/s/s. This is like our previous model of accelerated motion in free-fall.
All velocity vs. time graphs have a slope of about -9.8 m/s/s. Again, this is like our previous model of accelerated motion in free-fall.
Also…
The mass of the ball doesn’t matter. Again, this is like our previous model of accelerated motion in free-fall.
Projectile motion is simply the combination of the constant velocity model (horizontal) and the acceleration motion model (vertical).
Presenting lab results
Application
We are now ready to return to the Kobe Bryant video to apply the student’s newly created model for projectile motion. They decide to immediately feed the video into Logger Pro for analysis. Students are able to make a claim regarding the realness of the video, and justify that claim with evidence and reasoning. I ask them to accumulate as much evidence as possible in order to make a stronger case for their claim.
Groups that finish early are pushed further with more questions: Is Kobe’s horizontal speed reasonable? Is the vertical and horizonatal distances he leaps reasonable? How will you figure those out and make a claim to their possibility?
At the end, groups whiteboard their work again, groups present their results to the class, and we reach a class concensus. The debate here sometimes gets very heated.
And when they are all done, they still ask me, “Is it real?”
“You just figured it out yourselves!” I say. (*sigh*)
Notes
1. Robert Karplus workshop materials on reasoning and the learning cycle.:
2. If you don’t have Flipcams, a regular digital camera that shoots movies will do fine. And if you don’t have a digital camera, there are plenty of pre-fab projectile videos to use — have a look at Dolores Gende’s collection of physics videos for analysis.
3. Levels of Inquiry. This cycle has elements of both guided (Level 2) and open (Level 3) inquiry. I stay away from confirmation/verification (Level 0) at all costs. The coupled-inquiry cycle is an easy way to do more open inquiry in class.
Action-Reaction 