In a previous post, I wrote about a new term I had read about in Adam Grant’s best selling book Originals.
The term was vuja de, the opposite of deja vu. As Grant explains it, “Deja vu occurs when we encounter something new, but if feels as if we’ve seen it all before. Vuja de is the reverse – we face something familiar, but we see it with a fresh perspective that enables us to gain insights into old problems.”
Well I had a vuja de moment today.
I was doing my calculus homework, and I came to the problem you see at the top of this post. It immediately brought back memories of my college days.
It was my sophomore year, and I was a math major. I was in my dorm room doing my Calculus 3 homework when I came across almost the exact same problem pictured above.
Back then, I had no idea how to do the problem, but perhaps more importantly, I had little interest in figuring out how to do such a problem. And it was just a few days later that I made the decision to change majors to phys ed. I’ve always remembered that moment, sometimes with regret. And it was all because of a projectile.
Well my attitude today when I came across the problem was much different. Grant’s definition of vuja de fit almost perfectly: we face something familiar, but we see it with a fresh perspective that enables us to gain insights into old problems.”
I was highly motivated to solve the problem today, not because of any inherent interest in working with projectiles someday, but because of the challenge/fun of seeing how to apply calculus to a real world problem.
The problem still took me a bit longer than it probably should have, but I eventually figured it out, and I’ll admit there was a nice sense of accomplishment when I completed the problem.
I’ll also admit I’ve been waiting for this type of problem to crop up since I began taking Calculus classes last year. As I said, when I first came across such a problem 40 years ago, it became one of those moments that I’ll always remember. I was curious how I would respond when I saw it now, 40 years later. I’m happy to report a much better outcome this time around.
It reminds me of the George Bernard Shaw quote that “youth is wasted on the young.”
Perhaps education is as well…
P.S. By the way, this sort of calculus problem was in the news just last week. When North Korea fired a missile last week, it made a claim that it could reach the United States.
Here’s an excerpt from an NPR interview with David Wright, co-director of the Global Security Program at the Union of Concerned Scientists.
“A ballistic missile is only accelerated and powered for a couple minutes early on. And then at that point, it basically just travels through space under the effects of gravity. So it’s very much like throwing a baseball. It’s powered when it’s in your hand. And the speed and the direction that it’s going when you let go of it determines where it goes to. And so by making it go faster and faster, just like when you’re throwing a ball, you can make it go farther and farther.
They launched this missile essentially straight up. It came down, landed in the Sea of Japan. That has the advantage that it doesn’t overfly Japan, which has caused problems in the past. So by doing a computer model that asks what it would take for a missile to follow the flown trajectory, I can then use that same model to say OK, if I now flatten out the trajectory, how far could it go?.
And according to Wright’s calculation, the missile would cover Alaska, but it would still be a few thousand miles short of reaching the lower 48 and the West Coast.
Let’s hope that calculus has also figured out a way to intercept such a missile while in flight. Maybe that will be in the next chapter, the one I never got to 40 years ago…
P.S.S. In case you are interested, the projectile traveled about 3,535 meters, the maximum height reached was 1,531 meters, and the speed at impact was 200 meters/second.