guide Crash Course Parkour Physics: Kinematics

[Person_Random 4,991]

From the moment I first saw a team of tanks create breathtaking tricks on the V-Log to today, I have always been fascinated with parkour.  Learning physics only made me even more attached to this amazing application of Tanki’s game mechanics, and I’m here to share what I’ve managed to gather together after some research.

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Hello and welcome to a new series: Parkour Physics! In the next few articles, I hope to explain the secrets behind parkour. In each episode, you will find an ample supply of physics lessons and an explanation of the physics behind various aspects of parkour. There's so many things to cover, but of course, let’s start from the basics with the building blocks of physics: kinematics. If you're already familiar on this, continue reading - there's no harm in getting a refresher on physics.

 

 Warning Label (Please Read before continuing)

To interpret this document, it is best that you have some background in trigonometry and algebra.  I will do my best to explain the non-physics mathematics. Please contact me through Forum PM if you have any issues.

 

Kinematics, what’s that?

 

Kinematics is the branch of physics that deals with the motion of objects - specifically, in this case, tanks.  There are two types of motion that we’ll be dealing with: linear (translational) and rotational motion. Today, we'll be discussing linear motion.

 

Position and Displacement

Let’s start off with position, which is fairly simple: it is where the object is located.  For example, when a tank is at the Red Base in Forest, it is in one position, but when it moves to say, the Blue Base, it is in another position.

 

The change in position is then called the displacement.  However, while the tank may have taken one of several different paths and traveled different distances, the displacement is a vector with a magnitude equal to the shortest distance from the initial position to the final position.  In this series, I’ll be using meters for displacement and distance. Down with the imperial system!

An important point to note: distance can be the same as displacement, but they are not always the same.  This next example helps explain the difference.

 

Example 1

In this example, assume that the tank takes a completely square path 100 meters long on each side.  If a tank were to start on the Red Base of Sandbox, drive to the Blue Base and take the flag, and return to the Red Base, what is a. its distance traveled and b. its displacement?

 

Explanation

Spoiler

 

a. The distance traveled would be the square path.  Since the tank goes around the full square, all that’s left to do is find the perimeter, which is 4 × 100, or 400 meters.

b. The displacement would be the difference from the original position to the final position.  Since the tank starts off at the Red Base and finishes at the Red Base, its original and final positions are the same and therefore, the displacement is 0 meters.

 

 

Speed and Velocity

In the previous problem, the tank didn’t just move across the map instantaneously or else we’d call that hacking and report it to the Game Violations Section. It did it over a course of time.  Speed and velocity help measure how fast an object moves.

 

The average speed of an object would be the distance over time, while the average velocity is the displacement over time. Again, proper units: both speed and velocity are measured in meters per second. Let’s go back to that first scenario.

 

Example 2

In this example, assume that the tank takes a completely square path 100 meters long on each side.  If a tank were to start on the Red Base of Sandbox, drive to the Blue Base and take the flag, and return to the Red Base in a time of 50 seconds, what is a. its speed and b. its velocity?

 

Explanation

Spoiler

 

a. The speed of the tank is its distance over time. The time is stated as 50 seconds and the distance was found to be 400 meters.  Divide the numbers accordingly, and this comes out to 8 meters per second, about the speed of a Hunter M1.

b. The displacement of the tank is its displacement over time.  Since its displacement is zero meters and the time elapsed is 50 seconds, zero over 50 gives a final value of… zero meters per second.  You didn’t think it would come out to a different number, did you?

 

 

Acceleration

Again, just like how the tank didn't just teleport from one base to another, it didn't immediately go from stationary to top speed.  This is where acceleration comes in.  Like how velocity is the change in displacement over time, average acceleration is simply the change in velocity over time.  But before you move on to an example problem, let's just get those units sorted out: acceleration is measured in meters per second squared.

 

Example 3

A Wasp M0 starts from rest and reaches a top speed of 10 m/s in 0.6 seconds.  What is its average acceleration?

 

Explanation

Spoiler

Average acceleration is the change in velocity over time.  The final velocity that the Wasp reaches is 10 meters per second, while it starts from rest, or zero velocity.  Divide 10 meters per second over 0.6 seconds, you get a value of 16.66 meters per second squared.

 

(Bonus) Kinematics Formulas

If you're already bored at this point, it's probably a good idea to just chill and play some Tanki, because it's time to introduce the academic stuff.  Here's some kinematics formulas that will one day be useful in your life, if they aren't already.

 

 

Example 4

A Wasp is racing at a constant speed of 10 m/s towards the enemy flag in Magistral when he hears the Gold Box Siren and runs up the bridge. As the gold is falling, a Mammoth conveniently parks itself at the drop site. When the Wasp is four meters away from the Mammoth, it activates its overdrive. Simultaneously, the Wasp decelerates at a rate of -15 m/s². Will the Wasp be destroyed? (assuming that there is no interference, the Wasp takes no other damage, and that the Mammoth stays still)

 

To answer this question, let’s first find the variables in this equation.

Initial Velocity: 10m/s

Acceleration: -15m/s²

Final Velocity: 0m/s

The last value is implied, as the Wasp must come to a stop, either by being destroyed by the Mammoth or by stopping by itself. These variables fit in perfectly in the equation . (Yes, I happened to use x instead of s, these variables are interchangable.

 

Next, let's solve.

Good news, the Wasp will not be obliterated by the Mammoth. (but who knows what other havoc could occur within those short seconds)

 

2-D (and 3-D) Kinematics

At this point, I've only discussed kinematics in one dimension, where a tank moves on somewhat a 2-D plane without vertical displacement. But Tanki (and the real world) isn't like this.  There's much more to Tanki than just one-dimensional movement. Kinematics in two dimensions might seem a little complicated, but in reality, all you need to do is treat each dimension as independent, which will make problems and life much, much easier.  Here's an example problem.

 

Example 5

A team of tanks are trying to reach a square (20m by 20m) 9m tall building. The support team launches the jumper off at an initial velocity of 25m/s, 37 degrees above the horizontal, 20 meters from the closest side of the building.  Does the tank land on the building?

 

First, let's find out the variables in this equation, sorting them by the x and y components to facilitate the problem solving process.
 

Spoiler

Initial Velocity: 25m/s,

Initial Velocity (x-component): 25m/s(cos37) = 20m/s

Initial Velocity (y-component): 25m/s(sin37) = 15m/s

Acceleration (y): -10m/s² (implied, the acceleration due to gravity in Tanki shall be assumed to be the same as on Earth, -9.8m/s², which rounds to -10)

Building Height: 9m

Tank Distance from Building: 20m

Building Length: 20m

Whew, adding another variable (and another object) made this a whole lot more hectic. Solving this problem will be an adventure, to say the least.  First, let's find the height of the tank at its peak height. According to one of my secret knowledge sources (also known as calculus), this occurs when the velocity in the y-direction is zero.  Since the acceleration and initial velocity is known, and the objective is to find the displacement, the second equation fits perfectly. Let's solve.

 

Therefore, the tank clears the the building at its highest point, which also happens to be the middle of the building. Let's check the heights at the sides of the building, which have an x position of 20 and 40 meters, respectively. Here, I'm desperate to finish this article before Flexoo locks me in the mult dungeon, since the velocity in the x-direction is 20m/s, we can take a shortcut and get times of 1 and 2 seconds for these positions. Now, we can plug both values into the third equation.

  

 

Since the heights at the edges of the building and at the center of the building are over the height of the building, the tank completely misses the building.

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And that's all for this issue!  Thanks for sticking around and reading this article, and I hope to see you next time when I cover forces.  In the next episode, expect to see a in-depth explanation about why M0 (ahem, Mk1) Wasp is the superior parkour machine.  See you all next time!

 

[kaisdf 3,320]

For a fascinating and in-depth review of everything about parkour and how it works, enjoy this full analysis of the physics behind parkour by Person_Random.

[Sacrifice 2,278]

I hope PR wont mind doing my physics homework... 

[Mular 145]

Bloody hell...

[foxer_XXX 135]

Well, at least we know that someone likes math

[0tsutsuki 21]

Kinematics doesn't deal with the cause of motion so I believe just studying kinematics isn't enough. I hope that 'I'(one) really means we get more posts like these.

Pst: Seems like finally I can get something interesting on Tanki this year after all those crappy p2w updates

[Pythor 1,354]

One question PR... What happens when the X asymptote equals the limit of Y's fifth derivative? 

[Sacrifice 2,278]

Just now, pythor20000 said:

One question PR... What happens when the X asymptote equals the limit of Y's fifth derivative? 

My mind is having a shutdown. Needs sotware update and preferably a good antivirus renewal. All thanks to this comment. 

[ILiveOnTheChatBox123 936]

On 12/12/2019 at 11:00 AM, Person_Random said:

Example 5

A team of tanks are trying to reach a square (20m by 20m) 9m tall building. The support team launches the jumper off at an initial velocity of 25m/s, 37 degrees above the horizontal, 20 meters from the closest side of the building.  Does the tank land on the building?

 

On 12/12/2019 at 11:00 AM, Person_Random said:

Since the heights at the edges of the building and at the center of the building are over the height of the building, the tank completely misses the building.

You forgot the main point! "Therefore the team decides to do a different maneuver instead." It doesn't help if you just know the math, you have to carry it out! The NYS Regents uses this trick often, on multiple-choice questions, where after you calculate the solution your work matches one of the answers. The problem is you have to plug your work back into the example to get the correct answer. It can really be annoying.

This reminds of a joke: Three people are sleeping in different locations when there is a fire by all of them. One is a fireman, one is a physician, and one is a mathematician. They all have a bucket of water in their room. The fireman wakes up, grabs the bucket, and puts out the fire. The physician smells the fire, wakes up, grabs the bucket and puts out the fire. The mathematician wakes up, makes a quick calculation, decides the water in the bucket is enough to put out the fire, and goes back to sleep. (leaving the fire burning)

[ILiveOnTheChatBox123 936]

On 3/28/2020 at 6:46 PM, pythor20000 said:

One question PR... What happens when the X assymptote equals the limit of Y's fifth derivative? 

I know this was a joke, but an assymptote is the number the tank will get closer and closer to it, but it will never hit it. Due to gravity there are no assymptotes in such a case. You need an exponential equation, but since you don't usually have negative numbers in Tanki, it may be hard to find.

[Gauss-Hornet 489]

1 hour ago, ILiveOnTheChatBox123 said:

I know this was a joke, but an assymptote is the number the tank will get closer and closer to it, but it will never hit it. Due to gravity there are no assymptotes in such a case. You need an exponential equation, but since you don't usually have negative numbers in Tanki, it may be hard to find.

The Y co-ordinate varies as a function of time as

Y=f(t)=(u×sinθ)t-1/2×g×t²

While the X co-ordinate varies as

X=x₀+(u×cosθ)t

Pythor wanted to ask what happens when the value of X approaches the value of the Limit of the Fifth derivative of Y, or basically the limit of f'''''(t) or d⁵y/dt⁵ which, obviously, is 0.

Hence, its Limit is also 0. (No other value possible.)

The X asymptote equalling zero is just a joke as it's not a function that seems to near 0 but not actually reach it. It just varies linearly with t.

[Person_Random 4,991]

On 3/28/2020 at 1:36 PM, 0tsutsuki said:

Kinematics doesn't deal with the cause of motion so I believe just studying kinematics isn't enough. I hope that 'I'(one) really means we get more posts like these.

Pst: Seems like finally I can get something interesting on Tanki this year after all those crappy p2w updates

Ah yes, you are correct here. This is why I'll get into forces and energy as well. That'll be coming soon!

On 3/30/2020 at 4:46 PM, ILiveOnTheChatBox123 said:

 

You forgot the main point! "Therefore the team decides to do a different maneuver instead." It doesn't help if you just know the math, you have to carry it out! The NYS Regents uses this trick often, on multiple-choice questions, where after you calculate the solution your work matches one of the answers. The problem is you have to plug your work back into the example to get the correct answer. It can really be annoying.

This reminds of a joke: Three people are sleeping in different locations when there is a fire by all of them. One is a fireman, one is a physician, and one is a mathematician. They all have a bucket of water in their room. The fireman wakes up, grabs the bucket, and puts out the fire. The physician smells the fire, wakes up, grabs the bucket and puts out the fire. The mathematician wakes up, makes a quick calculation, decides the water in the bucket is enough to put out the fire, and goes back to sleep. (leaving the fire burning)

Ah, good point, thanks for the reminder. I guess I was so into physics I forgot about making sure I followed the math processes. I'll keep it in mind during the next episode.

[sensei_tanker 3,098]

This surely will be useful for my AP Physics Exam in less than a month.

[ILiveOnTheChatBox123 936]

On 4/13/2020 at 4:32 PM, Person_Random said:

That'll be coming soon!

Can you please make a part 2? (Maybe do one in time for your B-day?)

[Person_Random 4,991]

13 hours ago, ILiveOnTheChatBox123 said:

 

Very good idea! I've got Part 2 lying around somewhere... will see if I can bring it back Friday.