The physics of construction jumps in 'The Matrix'

Expect. You have not seen The matrix? It's a clbadic of modern science fiction that is now 20 years old. Well, you should watch it. Here is the basic idea: a guy (Neo) discovers he lives in a computer program. Since his world is not "real", he is able to do superhuman things – like avoiding bullets and dodging bullets and jumping from one building to the other.

Yes, this construction jump is what I want to watch. This is one of the first real tests for Neo who is learning to manipulate this computer world. The goal is to run and jump from the top of a very tall building to the next building. Morpheus begins to show Neo how to do it and makes it easy. Neo hangs. It's a good thing that it's not real life.

Even though it's only a computer simulation, it's still fun to see how a human could make that jump. Let's review two possible methods to perform this jump (in the matrix).

Run really fast

A normal human could not do this building to building jump in the real world. But what if you could run faster? How fast should you run to make that jump? Of course, the first question: how far are the building? I will be honest. I spent a lot of time looking for these EXACT buildings in real life. I have failed. However, it seems that it is only two normal buildings in front of one of the other. From my measurements from real buildings (on Google Maps), I think 25 meters seem right.

So how fast do you have to run to jump that far? Assuming that the air resistance is negligible, it becomes a standard projectile motion problem of physics. Once Neo is in the air, the only force that acts on it is the gravitational downward force. This means that its horizontal speed is constant and its vertical acceleration is -9.8 m / s² (We call it -g)

Horizontal and vertical movements can be treated as two distinct kinematic problems to produce the following equations.

Although the horizontal and vertical movements are mainly independent, they always occur at the same time (t). If I solve for total time in one direction, I can use it in the other direction. That's what I'm going to do.

OK, so in this case, I'm going to badume that the human (computer model of a human) runs very fast. At the edge of the building, the human lifts off the ground to launch the jump. However, it's just a normal human running fast. This means that the vertical jump is always a normal jump with a normal vertical height. Let's say that the human can jump with a vertical height of 1 meter. This would give a suspension time of 0.6 seconds. Yes, I know it seems longer than that, but it is not.

Now let's go back to the horizontal movement. Neo has only 0.6 seconds to go from one building to the other. With a distance change of 25 meters in just 0.6 seconds, he has to run at a speed of 41.7 meters per second (93 mph).

I told you that it was really fast.

Jump really difficult

Yes, it looks like the previous jump method. However, in this case, the launch speed of the human will be vertical and horizontal instead of just running fast. This means that Neo will stay in the air more than 0.6 seconds to not have to reach such a high horizontal speed. But that also means that he's going to need a human push on the ground to make him fly.

This human jumps with an initial speed of v₀, but this means that there is a speed component in the x direction and the y direction which depends on the launch angle. Which angle is the best? Well, maybe this is not the best but if you want the maximum horizontal range for this speed, the angle should be 45 degrees. Why? I will leave this older version here, but you have to be careful. A 45-degree launch angle is only the maximum range for cases that begin and end at the same height (flat ground). In addition, it does not work if there is air resistance on the projectile. You were warned.

Since this case concerns "a ground level" and no air resistance (because I have said it), I can easily find the launch speed to travel a horizontal distance of x₂ (baduming this starts at x = 0).

For a distance of 25 meters, Neo should jump at a 45 degree angle with a launch speed of 15.6 m / s (34.8 mph). This is not humanly possible, but at least it's a slower speed than just running.

Change the gravitational field

The matrix is ​​not real. So why should anyone coerce themselves to real things? Instead of running fast or jumping fast, you can simply change the gravitational field. The gravitational field is the force per unit mbad on the surface of the Earth. We usually use the symbol "g" for this and it has a typical value of 9.8 Newtons per kilogram. But if you drop (or throw) an object, the force (weight) and acceleration depend on the mbad of the object in the same way. This means that all falling objects have the same vertical acceleration of 9.8 meters per second squared (corresponding to a unit equivalent to N / kg).

If you decrease this gravitational field, you should be able to jump further. But what value should you use if you can change it? Why not look at the successful Morpheus building jump? From the video, it takes about 4.2 seconds to complete the jump. If I suppose that it jumps like a normal human with an ascending speed of 3 m / s (this would give a suspension time of 0.6 seconds), then the gravitational field would be 1.4 N / kg. Oh, it's about the same gravitational field as the moon's surface (1.6 N / kg). Maybe that's how Morpheus does it. He's just pretending that he's on the moon.

If you need homework, how about repeating these three calculations while including air resistance? It would be fun.

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