Anime Mythbuster: Jumping

Now, we all know that Physics in Anime is, for the most part, very unlike our own. However, often viewers will immediately dismiss their observations as impossible on our world, without any actual analysis. Now that’s not very scientific! So to save everyone else the time of doing this (and I am sure that everyone was, or was planning on doing this), I have done a small physical analysis of one such instance of Anime physics.

Now let us set the stage!

NOTE: I have several diagrams and equations in links. Please see them to better understand what I am talking about at that moment.

I believe that a very typical, and rather easy to analyze, situation is that of many characters’ extraordinary jumping ability. So let’s use Kenshin (of Rurouni Kenshin fame). Kenshin, off to save another would-be victim of Shishio, does not want Yahiko following him, afraid for his safety. As such, he decides to jump onto a nearby house, and continue onwards above the ground:

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So, we have a house, let’s say 3 meters high, and Kenshin, who is, for argument’s sake, 1.6 meters tall (not that it actually matters for this problem), and weighs 50 kilograms. Now let’s draw a free body diagram of Kenshin at rest, and just to note, from now on we are considering Kenshin a point mass (as his mass is what matters, not his physical dimensions such as height).

If you don’t know what a point mass is, just imagine that Sanosuke, angry at Kenshin for running off without him, pounds Kenshin into a very small ball (don’t worry though, Kenshin is still alive. He IS Kenshin after all).

Just a small explanation of the force diagram: Normal Force is the force that is exactly equal and opposite the Gravitational Force (the force gravity is exerting on an object). It does not really matter that you understand what it is for this problem, so you can just ignore it if you do not understand.

Now, using Newton’s 2nd Law, let us calculate the current force on Kenshin (this is not necessary, but let’s do it anyway, just so that well all know what it is, as this equation will be needed later). Newton’s 2nd Law states that the Force (not from Star Wars, sorry fans) on an object is equal to the Mass of the object, times the Acceleration it is experiencing. Commonly it is written as F=ma. Just think of Fullmetal Alchemist (FMA), and you’ll remember the equation.

So let’s do the calculation of Kenshin at rest. Kenshin’s mass is 50 kg (kilograms). The current acceleration on Kenshin, though he is “at rest”, is the acceleration due to gravity, measured at 9.8 meters/(second*second), or 9.8 m/s^2 (9.8 meters per second squared). This is an acceleration that always exists on each one of us as we move around on the Earth. So even though you may be just sitting in your chair in front of your computer right now, you are in fact being “pushed down” by gravity, due to this acceleration.

So doing the calculation, we see that the Gravitational force on Kenshin is 490 Newtons down (Newtons are (kg*m)/s^2, kilogram meters per second squared). And since we know this, we also know that the Normal force on Kenshin is 490 Newtons up (equal and opposite force).

OK, so now we know what Kenshin is doing right now: he is getting ready to make the jump up to the house, but currently at rest. But how high is Kenshin getting ready to jump to? Sure the house is 3.0 m (meters) tall, but if Kenshin only jumped 3 m, that would be cutting it close, and may hit the house!

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So let’s say that he will jump 3.2 m, just to be safe.

Another note: we will not worry about Kenshin’s horizontal distance that he needs to travel to make it onto the house, as it is not needed for what we are concentrating on. So when Kenshin jumps up, just imagine that someone pushes him in the air to make it to the house, or something to that effect.