Mario, DON'T JUMP! Calculating the Danger of the Yoshi Sacrifice! | The SCIENCE of... Mario

Are you tired of dying while trying to make those

danger

ous long

jump

s? Are you riding a Yoshi? Then worry no more, young friend! I just tried Yoshi's patented

sacrifice

! Simply press the

jump

(spin) button to send your cute friend, who saved you from being eaten by Koopas when you were a baby, throwing him into the abyss as you arrive safely at your destination! That's Dr. Hourigan's Yoshi's Marvelous Sacrifice, available now at your favorite nickel and diamond store Dear Nintendo, Hello, it's me: Austin! And today what I have on my agenda to ruin your childhood is Mario 'jumpman' Mario, amphibian killer extraordinaire, and I'm going to focus on something really specific;

Yoshi's

sacrifice

. This is a movement that originates in... *God will make me feel so old* 1990. Almost 30 years with the introduction of Yoshi to the Nintendo franchise in Super Mario World. Since then, it's more or less become such a long-lived trope that it's appeared in almost every game where you can ride Yoshi if you want, it's a recurring staple in the Dorkly Bits shorts, it has several Super Mario levels Maker dedicated to using this mechanic and it even has its own song, and it's been my absolute and complete obsession for the past few weeks and I've been focusing my laser-vision scientific brain on this problem because it's deceptively complicated.

It's a great example of the fun things you can do with basic Newtonian physics, and since this problem keeps me up at night, keeps me up at night, and writes on the walls like a madman in the middle of the night when it's very busy. paper. thrown everywhere. This is the madness to which I am going to subject you so that you can accompany me into the abyss of kilograms, meters and seconds per Newtonian second. Okay, so the base, okay, let's review. This is a Newtonian physics problem, no pressures, no relativity, just basic masses, accelerations and velocities, which means we have three main rules to keep in mind.

The three laws of motion, as set forth in Sir Isaac Newton's treatise Philosophiæ naturalis principia Mathematica, and are as such: omnipresent corpus Enough! You literally made the exact same joke less than a year ago in the Super Smash Brothers episode. Bad Austin! It's okay, it's okay. You're right. Well. Very quickly, the three laws of motion are: (1) An object remains at rest or continues to move at a constant speed unless acted on by an external force. (2) The rate of change of momentum of a body is directly proportional to the applied force and this change of momentum takes place in the direction of the applied force.

And (3) When one thing applies a force on another, that 'something else' exerts a force on the first thing. These three ideas are all we need to find out if this Yoshi sacrifice jump is possible. And that is correct. I said possible, because the first hurdle I thought of was, well, this is a closed system. Is it possible for Mario to jump and change his speed if he is part of a closed system in the air? And to answer this question, we need to do a thought experiment. Imagine instead that Yoshi and Mario were floating in orbit...

Okay, no way. Well. They have space suits on *okay, okay, that's better*. Anyway, if Mario pushed Yoshi, could he float away? And the answer is yes. He would do. The important thing is that not only would Mario float away, but he would also send Yoshi floating, because to move, he would have to create an equal and opposite force, so Yoshi would float in the other direction. You can even try this for yourself if you want. Just grab something for your table or whatever, jump in the air and while you're in the air, throw whatever you grabbed into the air.

I chose a pen when I did and there are two things worth noting. One: it's surprisingly difficult to time your throw correctly, and two: the pen, although it may not seem like it, actually makes me fall to the ground faster than I would have if I hadn't thrown it, since it's exerting a downward force on my body to be able to rise. This will be very important later. Well. Then the jump is possible. End of episode I guess! Hey, oh, wait, no, no, no, because this maneuver is much more complicated than two objects floating in space or me taking a photo in my apartment.

There are a lot of factors here, so let's start with the simplest step first, the physics of Mario's jump, and then we'll go from there. Well, here's Earth and here's Mario, and since Super Mario World is the first game to have Yoshi's sacrifice mechanic, this is the game, whenever possible, that we'll do all of our measurements in, like this! that! First things first, we have to jump. Good job buddy! Using the height of Mario's cannon, 1.55 meters, we can calculate exactly how high he jumps each time in this game: 3.69 meters. It takes 0.5166 seconds to reach maximum height and it takes 0.45 seconds to accelerate down and touch the ground.

With all the information we can calculate the surface gravity of the game, which is 36.419 meters per second squared, almost four times the gravity of the Earth. Now the flags among you are going to point out that Mario reaches a terminal velocity where he no longer accelerates, and that all the downward acceleration occurs in the first few seconds while he falls, to which I say, if we stick to that metric, the surface gravity of our world would be more than two hundred and forty meters per second squared or more than twenty-three times the surface gravity of the Earth.

That's more than ten times the surface gravity of Jupiter, so it's thirty-six point four! But this is where the fun part begins, because knowing all this, you find out Mario's initial speed when he leaves the ground, which is important because after his feet leave the ground, Mario can no longer impart any real energy to his body. , and its speed is fixed and the only thing acting on it (aside from the negligible air resistance) is the downward force of gravity. Fortunately, all we have to do is take this formula that equates potential and kinetic energy and rearrange it so that our unknown velocity is on one side. mass cancels out and we get the square root of two times the gravity, which we have, times the height, which we also have, all of which gives us a result of sixteen point three eight meters per second or 36 miles per hour.

That's a big leap, but we're not done yet because all this work only gives us one piece of a three-part puzzle. We need to figure out what we really want for reasons that will become clear later, what Mario's strength is. exerting on the ground, and for that, we will need force equal to mass times acceleration. You see, when you are standing on the ground, you are actually exerting a force on the ground. But let's simplify this. A 1 kilogram mushroom sitting on the ground in the Mushroom Kingdom is exerting a force on that ground, which is mass multiplied by the acceleration due to gravity, one times 36.4, is 36.4 newtons.

The soil, in turn, obeys Newton's third law: it exerts an equal and opposite force on the mushroom, creating a net force of zero, allowing the mushroom to remain still. In order for it to jump, well, it would have to grow legs, but let's imagine that it can jump without them. You will have to exert a force on the ground greater than the force of gravity. If you exert just 38.4 Newtons, the ground will push back with a force of 38.4 Newtons, giving the mushroom a net upward force of two Newtons once gravity is subtracted, which is enough to cancel the attraction of gravity and accelerate the mushroom upwards at enormous speed. 1 meter per second per second is not very impressive.

But acceleration, strength, these things take time to really mean something to us. And in fact, force equals M*A can be written by hand as force equals mass times the change in velocity over time to get meaningful data on Mario's jump and the amount of forces exerted on the body. of the. We need to know how long it lasted. leads him to jump. We need to know this for several reasons; If we look at that mushroom again... If you put it in a vacuum and push it with 2 Newtons for 1 second, it will accelerate at 2 meters per second.

But if you apply that force continuously forever, it will reach speeds close to the speed of light in less than 150 million years. *pause* Hello everyone, future Austin, here from my desk. While editing this video, I realized that I made a mistake and had actually made it in the past, and instead of just fixing it, I thought I'd explain what happened real quick before anyone says anything. I mixed up my units because I simply divided the speed of light by two for the acceleration, and the problem is that that gives you 149 million seconds, because the acceleration is in meters per second.

The reason I thought it would be interesting to talk about it. This is because a lot of people mess up their drives when they start doing these types of calculations, and I wanted to show the errors they can cause and how easy it is to do so. So if you actually divide it by the number of seconds in a year, which is 31 million five hundred and forty (thousand) seconds, you get four point seven five years, which is a big difference from 149 million years. Anyway, I wanted to correct that. Onward with the episode! *resume pause* ...Millions of years!

In short, to know how much force Mario exerts in his jumps, we need to know how long it takes him to reach the speed of sixteen point three eight meters per second, and although the games have perfect reaction times and he jumps instantly, this would create incredibly high forces . A more realistic model, determined experimentally by athletic scientists, suggests that vertical jumps impart force to the ground over the course of approximately point five seconds, meaning Mario goes from zero meters per second to sixteen point three eight in just 0.5 seconds, what it gives takes us, finally, to an acceleration of thirty-two point seven seven meters per second.

Now we just need Mario's mass, which a while ago I discovered was eighty-nine kilograms, using literal rocket

science

, which gives Mario's jumping force a whopping two thousand nine hundred and seventeen Newtons. MATH! *Loud exhale* Now that you know the basics, let's get back to Yoshi, because this is where things get really interesting. In fact, we have to calculate two separate values ​​because Mario can jump off Yoshi at two different points; He can jump to the maximum jumping height, which is the most feasible, but the most terrifying. He can jump just as high while falling at a terminal velocity, and even scarier, I discovered that the height difference, that's the difference from his feet at the start of the jump to the top of the jump, is actually higher if he jumps from Yoshi .

For some reason, Mario can jump over fifteen feet if he jumps off Yoshi's back. Oh wow, this gives us an initial velocity of 20.5 meters per second which we have to reach in just point five seconds. Now, at the highest point of Yoshi's jump, this means that he is exerting 3615 Newtons on poor Yoshi's back, and this is where things get out of control, because remember, objects exerting forces on other objects create a equal and opposite force. The pen in my hand pushes me down, remember, and makes me fall faster. Imagine a nearly 200 pound plumber jumping off my back into the air.

That's going to make me FLY. And in this case, I am Yoshi. Yoshi would fly down, but by how much? Well, that depends on Yoshi's mass. Is Yoshi the pen or Mario the pen? And finding the answer to this was not easy. Mario Kart puts Mario and Yoshi in the same weight class, so they're probably pretty similar, but that's not saying much. Finally, I figured it out. If we can find an object that exerts uniform forces on both, we can determine how much more one weighs than the other, if anything, based on how much they move.

Yes, that object exists and it is the trampoline. Unfortunately, the trampoline in Super Mario World doesn't affect Yoshi if you don't mind, but it does affect Yoshi independently in Super Mario Maker. Mario Maker isn't exactly the same size as Mario World, but the physics are scaled almost perfectly pixel by pixel, with a margin of error of about 5 percent. It's not perfect, but it's what I have, and guess what? They appear at different heights when left alone. Yoshi rides about 16% taller, which means he weighs sixteen percent less than Mario, which means he weighs about seventy-four point six kilograms, which is bad news for this little guy, because he's already going to begin accelerating downward at thirty-six point four meters per second per hour. second due to gravity, plus an additional forty-eight meters per second from the thirty-six hundred and forty Newtons that Mario is putting into it, which means it will hit the ground at a devastating speed of forty-two point six meters per second or more than ninety. -five miles per hour.

That's like a car accident. But! It gets even worse, because Mario can perform the same move while traveling downwards at a terminal velocity of thirty point seven five meters per second, which means that to jump five point seven seven five metersIt has to impart enough force to override everything. 89 kilograms of the plumber traveling down, and then enough to accelerate it even more! If we take Mario's initial speed of twenty point five and subtract negative thirty point seven five, his downward speed, we learn that his initial speed leaving Yoshi has to be 51 meters per second, or more than 100 miles per second. hour, which would require an acceleration of more than one hundred and two meters per second per second, which would require 9121 newtons of force, which would accelerate Yoshi 122 meters per second per second in the opposite direction, leading to a maximum net speed of over 91 meters per second, which is, get this, over 205 miles per hour!

That's like accelerating a McLaren F1 to almost top speed and then driving it straight into a concrete wall, and that's completely neglecting the pressures placed on Yoshi's back bones that would probably completely pulverize his spine just from the jump if the Falling wouldn't kill him, and furthermore, if Mario is able to exert 9,124 Newtons of force, then it would mean his top. The jump height from the ground must be greater than 36 meters, or one hundred and 18 feet! Why don't you jump like that all the time? So yes, it turns out that yes, this move is theoretically possible.

But no matter what happens, it's terrible for Yoshi. Mario is an idiot... I mean, whether it's being mean to his brother, sending his pets to die in bottomless pits, or sending them crashing into the ground faster than a bullet so they turn into dinosaur bones. . Mario is consistently the most evil character Nintendo has ever created, and that's the kind of fun stuff you can do with classic physics. Sincerely, Austin. You