Projectile Motion (WITH AIR FRICTION)

Typically when one studies projectile motion, they neglect air friction so that the solution becomes simpler. In this video, we look at projectile motion WITH air friction, examine various trajectories, and look at optimal launch angles (to send a projectile as far as possible) under different frictional forces.

Code:

Discord:

[frednalyanya]

Imagine I was taking about hours to learn through each video without knowing you had the code down the description! I was literally pausing and typing word by word. Today I just noticed there is a code(s) below. Again thank you for your great work!

[gregersiika]

Excellent work explaining this in a way that makes it accessible also for people with average math skill (like me...) Thanks to your tutorial I was able to apply this, to create a ballistic calculator that perfectly agrees with other commercially available calculators. This has been on my mind for many years and now, thanks to you, I was able to do it. I can't thank you enough! Keep up the good work!

[jcmschott]

Hey, Luke! Your tutos are always amazing, thank you so much!

[Hacker-at-Large]

Now account for lift due to backspin… 😀

[alboz]

We need to make this genius more popular.

[TheDuxbuse]

Would be interesting to compare a cannon or rifle.

Or even more spicy a laser (perhaps on an infinite surface?) though not sure if friction affects light.

[guillaume]

Hi thank you for the content you provide on youtube. I really would like to see the equation and the solution for projectile which is spinning, first with taking any magnus effect into account, I guess it does not stay in 2D due to gyroscopic forces

[abizair]

But why does it became -1-(bg/m)√(...)? Shouldn't the g now being squared, thus -g²-(bg/m)√(...)?

[jahanvi]

Thank you!!! This really helped me alot

[willh]

How would you amend your program to account for the variation of atmospheric density with altitude and also that your Cd value also varies with velocity. During my MSc we used MATLAB and Simulink to model projectiles but I am really interested to learn how to re-create it in python. Thanks for your content!

[АндрейМихайлов-эд]

I haven’t slept for few days straight and I have quite a low faith in my math skills right now, but is it right calculations or am I tripping? The coefficient in front of both square roots should be b/(mg) when you making accelerations dimensionless. Plus in latex formula for d Vy/ dt when you telling about lowering order of diff equations you missed -1 I guess. Cuz later in defining dSdt you have it. But again, I might be just tripping.

[henrymaynard]

Hey trying to code a 3D projectile with drag for my coursework, what library are you using?

[stevenmellemans]

Nobody noticed there is something fishy with the division by g?