Why you should wait to teach projectile motion part 1: the problem
This is part 1 in a 3 part series about how I’ve decided to move teaching projectile motion from one of the earliest units I teach, until after my students have a thorough grounding in vectors, Newton’s laws and momentum.
Projectile motion is the meat grinder of physics—more than any other topic, when adults or students recount the horrors of their experience with physics (this is a common conversation for most physics teachers) it centers around figuring out where an object hurled into the air at 30 m/s at an angle of 20° will land. If you examine the timeline of a traditional textbook, it’s easy to see why. Here’s how most of them go:
- Units and lots of boring crap. Yes, there’s a some platinum bar stored under vacuum sitting in France that we use as a a kilogram. The real reason for this is never fully explained, nor is the awesome story of all the efforts we’ve gone through to rid of that dumb bar. Many teachers just skip this whole unit.
- Kinematic equations. Yep, so you’re not really comfortable with albegra, and don’t really understand rates of change. Well, get ready cause it’s time to know the difference between a rate of change (velocity) and a rate of a rate of change (acceleration). And don’t forget, in physics world, acceleration can mean slowing down just cause we say so, and soon we’ll show you how you can even accelerate with constant speed. But for now you need to memorize these four (or five equations if you want to see how bad it gets over at sparknotes) equations:
Sure, the professor/teacher tries to show how these equations are all connected, and can be seen graphically, but students usually don’t get enough time to understand these ideas, and most of this stuff gets lost in a wave of tedious problem solving. Did I mention that many courses cover these topics in a week or less.
It’s quite possible that
is the most complicated equation students will see in first year physics. For the untrained eye, this looks like an equation with 5 variables, superscripts and subscripts?! It is truly a mathematical monster.
- Vectors. I hope you got those equations from the last chapter down, because now it’s time to learn that all those things you learned about in the last chapter have direction, and 2+2 no longer equals 4. Again, this can sometimes be covered in less than a week.Winded yet? In a college level class, you may have only been in class for 3 or 4 days and your head is swimming with all the deltas, vector symbols and equations. Learn fast, because it’s time for projectile motion.
- Projectile motion. Here’s where the wheels fall off the physics wagon for many students. You start by telling students everything falls at the same rate, a dropped bullet and a fired bullet will hit the ground at the same time, and that if you’re hunting monkeys in trees, it is best to aim at them. Why are these things true? Who knows? The equations are the important thing, so focus on memorizing those. Then it’s time for a lot of hard problem solving, which can get a bit easier if you always remember to use the constant velocity equations for the horizontal motion, and the constant acceleration equations for vertical motion. You did figure out the difference between acceleration and velocity in the past two days, didn’t you? I hope you really like systems of equations and are pretty good at sorting out these equations that seem to have so many variables. And here’s the real kicker, almost nothing you do in these calculations is true. The baseball hit at 30 m/s and 15° will never land where your calculation says it will. Subtlety, you learn that the world of physics and the world of reality have little in common. But don’t worry, you’ll only be doing projectile motion for another few days before many courses jump on to Newton’s laws.
The missing piece
The big problem with this treatment is it misses the beautiful picture of physics that many different phenomena can be explained with a small number of ideas. Falling bricks, hunted monkeys, batted baseballs, and even orbiting satellites can all be described with the very same principles. Why do the all objects fall with the same rate? Why should you shoot at the monkey? Why does the fired bullet hit the ground the same time as the dropped one? It’s because in all three cases, the objects are only experiencing the gravitational force, and this force is proportional to the mass of the object, so all projectiles will have the exact same acceleration. The only difference will be the parameters, starting position and velocity.
This is a subtle and beautiful idea that students can’t possibly get when they haven’t been exposed to Newton’s laws, and it is something that is hard to pick up if you’re flying through the standard physics text faster than most of the projectiles in the textbook problems.
While I’ve intuitively seen the pitfalls of the traditional approach to projectile motion for a while, I’ve found it very hard to break students out of the habit of approaching it from a traditional viewpoint. My students always want to default to equations to memorize, and this prevented them from having any real synthesis of the big picture, no matter how long I would wait to introduce projectile motion, and no matter how much I would emphasize starting with Newton’s laws to study it.
it wasn’t until this year, when I fully embraced modeling, that I came up with an approach to projectile motion that really seems to make sense, and gives students a strong feeling of the power of physics, and their ability to use it to understand the world. Modeling is a huge part of this, but it’s also a great opportunity to connect with computational thinking.
This will be the topic of parts 2 (Introducing projectile motion with Angry Birds) and 3 (Modeling real world motion with vpython) of this series.