My colleague is obsessed with ninjas in the same way I’m obsessed with superheroes. Whenever she gives her kids a challenging problem, she calls it a Ninja Problem. Students who gain ninja status in her class basically earn bragging rights. My first Ninja Problem went like this: “Is it possible to knock the goalie back into the net with a hockey puck? If no, what would it take?” (Hint: you can do most of the work using conservation of momentum.) Mad props to xkcd what-if for the inspiration.

H’s Hockey Puck Analysis

My student, H. took this Ninja Problem on with a vengeance.

After about 24 hours of thinking time, I shared a video with him that a Twitter pal shared with me. Fun and inspiration ensued.

Here’s his response:

Whoa! That’s crazy. I figured out that in order for a hockey player weighing 151 lbs (126 lbs for average 15 year old and 25 pounds roughly for average hockey gear (68.4924479 kg)) to be pushed .5 meters into a hockey goal in one second, a hockey puck must be launched at the average of the average velocity of a hockey puck (80-90 mph which I chose 85 mph (37.9984 m/s)) and after I calculated the volume of the hockey puck and its required mass, I found that the hockey puck must weigh 4.05729254 grams per cm^3 or .469969705 kg [ed: which is about 5 times heavier than a typical puck]. This means that it closer to Krypton and between Krypton and Yytrium. And in that video I think that guy was moving a little more than .5 meters per second haha. Thanks!

And 5 minutes later:

Whoops I have made a mistake! I multiplied took half of something while multiplying the other side by 2. The real answer is a hockey puck is needed to be made out of samarium or iron.

We talked through the effect of the goalie bracing against the ice (which H ultimately discarded because he didn’t know how to calculate for it), which made me wonder if he’d read the xkcd what-if answer. He hadn’t! When you get rid of bracing, it becomes much simpler to push the goalie back into the net.

N, K, and J’s Solution

This group of students, who elected one to be the star of the video, did a great job of separating the realistic scenario (which they quickly dismissed as implausible) from the hypothetical.

Implications for Physics Teaching

Mythbusters has made asking “what would it take?” fairly normal. A lot of my students understand the general approach of “ok, this thing is impossible as we’ve constrained it, so how could we reframe the situation so it’s plausible?” xkcd’s what-if extends on that. In fact, the hockey puck answer starts off with this gem:

This can’t really happen.

It’s not just a problem of hitting it hard enough. This blog isn’t concerned with that kind of limitation. Humans with sticks can’t make a puck go much faster than about 50 meters per second, so we’ll assume this puck is launched by a hockey robot or an electric sled or a hypersonic light gas gun.

Because high school physics often includes oversimplification to the point of absurdity, the “what would it take?” mechanism helps kids latch on to real problems in meaningful ways.

Points going forward:

1. Teach the kids estimation & rounding skills back-of-the envelope calculations, which don’t require such precision.
2. Find or write more of these questions!
3. Figure out how to engage more kids with Ninja Problems. This problem seriously engaged 5% of my students. I’d be thrilled if the number were closer to 20%. In Doing Whatever a Spider Can, I promised to get kids describing their assumptions more regularly. So far, I haven’t. Ninja Problems may be a nice way to engage kids in this process.