My Potato Gun Teaches You Differential Calculus

In this video we explore differential calculus in the context of finding the muzzle velocity of a potato gun. You don't need a speed gun or a chronograph, just a little physics, algebra, and calculus to estimate the initial velocity of the potato!
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
We use unique topics for algebra, trigonometry, calculus, and much more and go beyond context problems and use a technique called mathematical modeling to find solutions to real world questions and real world problems. These videos are great for students who plan to enter technical fields that require real world problem solving, and can be a great resource for teachers looking for ways to bring real world contexts into their classroom.
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Created by Doug Corey
Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media
© 2023 BYU

[@Anife69]

Thank you again math the world guy I really enjoy your videos

[@MathTheWorld]

Thank you! We're working on it!

[@natanprzybylko7227]

“Air resistance is negligible” is like music to my ears

[@Me-0063]

If you want a less theoretical speed measurement, you can use a camera, preferably higher fps, and measure the distance traveled through one frame using some kind of backdrop. Usually, stripes that alternate between black and white are used. Knowing the disyance between the change un color, you can measure the distance the potato travels over one frame. To find the time, you do 1/fps. You can then use these numbers to estimate the practical speed

[@MathTheWorld]

This is great! We had actually thought about adding this into the video too but felt it was long enough as is haha but a great way to find speed as well!

[@dougcorey3830]

That strategy is another great one to illustrate the ratio of small changes to calculate the speed. The math is the same as in the video, you just gather different data.

[@thefatcat2790]

for context: 933.3 m/s is about 2.74 times the speed of sound. You DEFINITELY don't want to get hit by that!

[@alocsx]

Potato math

[@MathTheWorld]

Well if we shot the potato at a grate then it would be french fry math.

[@kaaristotelancien3005]

(put anything you want) math

[@lingerlights]

Damn, I clicked on this video thinking that you will just draw two lines on a board, this is a much more interesting way to test the speed of it

[@carultch]

If you want to add a follow-up video to this, I have a topic to suggest. Consider the theory behind the muzzle velocity, as the gas expands while the potato accelerates. This produces a pressure vs volume curve, and the area under it, is the work done accelerating the potato. The work by friction of the potato against the walls of the barrel, subtracts from the work of the expanding gasses.
Adding onto this, it would be interesting to determine whether there is a length of the barrel that optimizes the muzzle velocity, or whether it would always increase, but eventually with diminishing returns.

[@MathTheWorld]

I actually thought of the optimal barrel length idea when I was trying to improve the velocity of the potato gun. I created the longer barrel but it was just a guess on what length might work well.
I agree that it would make a great video! We will put it on our ever-growing list.

[@wasordx3245]

Crazy how you got so little views and subs when your vid quality is this gud

[@MathTheWorld]

Thanks! It just launched so I'm hoping the views will pick up.

[@alistairmathie7632]

will definitely be using this to try teach calc to my nephew! thanks!

[@MathTheWorld]

Wonderful!

[@richardl6751]

For 45° d=v²/g Some distance is lost due to air resistance but it will give a close estimate for velocity.

[@donwald3436]

3:48 don't Darwin any birds either lol.

[@pop-tart2220]

I absolutely love your videos

[@Zirkorn]

splendid video, i love your channel sir!

[@MathTheWorld]

Glad you enjoy it!

[@captainpenny2122]

1.)Why couldn't we find the first derivative of the equation we got we got for the height with respect to time, then substitute values for time to get the velocity at any given time.
2.)If your potato is projected at an angle lets say theta to the ground, knowing the range, could you use Range = initial velocity squared multiplied the the sin of 2 times the angle all divided by the value of acceleration due to gravity. R = (v^2 sin 2θ)/g
Could be wrong though, these are just suggestions.

[@jcorey333]

This was really interesting! And firing that potato gun is pretty fun.

[@Space_and_history]

Now that’s what I call math overkill

[@dylanrapp7629]

Okay, but does it make French fries?

[@matthewjheaney]

Who is the person labeled Jackson?

[@prometeusze]

cool!

[@Space_and_history]

Now that’s what I call math overkill

[@Space_and_history]

Now that’s what I call math overkill