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Falling Sphere with Air Resistance Proportional to $v^2$
Developed by Kelly Roos  Published July 17, 2016
This set of exercises requires the student to generate a computational model of the 1D motion of a spherical object dropped from a tall building, and then graph and analyze the output of the model. It also guides the student in exploring the accuracy of a computational algorithm by comparing the computational results with an exact solution obtained analytically. The numerical approach used is the simple Euler method.
Subject Area  Mechanics 

Levels  First Year and Beyond the First Year 
Available Implementations  C/C++, Fortran, Glowscript, IPython/Jupyter Notebook, Mathematica, MATLAB, Python, Spreadsheet, and Haskell 
Learning Objectives 
Students who complete these exercises will be able to:
 model the motion of a falling sphere with air resistance in one dimension using the Euler algorithm (**Exercise 1**);
 produce graphs (position and velocity vs. time) of the computational solution (**Exercises 26**);
 assess the accuracy of the computational solution by comparing it to the analytical solution (**Exercises 2 and 3**);
 describe changes in the behavior of the model (e.g., time to approach terminal velocity) based on changes to properties of the falling sphere (e.g., mass and crosssectional area) (**Exercises 46**);
 describe ways to test the accuracy of a computational solution when there does not exist a known analytical solution (**Exercise 7**).

Code
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Credits and Licensing
Kelly Roos, "Falling Sphere with Air Resistance Proportional to $v^2$," Published in the PICUP Collection, July 2016.
The instructor materials are ©2016 Kelly Roos.
The exercises are released under a Creative Commons AttributionNonCommercialShareAlike 4.0 license