The goals for this project include one or more of the following:
- Using MATLAB with the dsolve and ezplot commands.
- Making use of script M-files in MATLAB.
- Using MATLAB along with if/then statements to perform approximation techniques, and bring in the plot command; or do the aforementioned in a spreadsheet (most likely Excel).
- In either a spreadsheet or with MATLAB, approximate a system of differential equations by tweaking previous files to adapt to the new problem.
The Project is:
Two identical capsules are manufactured; they are both attached to parachutes and have a compartment inside of them for a small payload. If they are falling, they experience a drag force numerically equal to .1 times the velocity. The capsules and parachutes have masses of 10 kg each.
One of the capsules is loaded with a 15 kg weight; this capsule (the heavy capsule) would now have a mass of 25 kg. They are dropped from a great height. Will they fall at the same speed? We know that if air resistance is absent, feathers will fall as fast as bowling balls. But with these two objects, which drag is affecting in the same way; will they fall at the same rate?
Their positions are the solutions to
with for the lighter capsule
with for the heavier capsule
Solve these initial value problems using MATLAB; discuss your observations. Include any graphs or other helpful information (screen shots, or the text of what you typed in, or any script M-files) should be attached; it's preferable to have all of this in one document, either a *.doc, *.docx, or *.pdf.