Name
Team Number
AAE 251: Introduction to Aerospace Design
Homework 0
Due Thursday 12th January 11:59 PM ET on Gradescope
Instructions
Show all the work. You will not receive full credit for a correct final answer if you don’t
show your work.
You must use the template provided. Anything that you want the graders to grade must
be within the boxes provided to you.
There are multiple steps involved to complete your submission on Gradescope. You can
follow the step-by-step guide posted on Brightspace. Complete all the submission steps
to make sure your assignment is submitted.
Make sure you scan all the pages of the assignment. Be extra careful if you printed on
both sides – make sure the scanner is set to scan both sides of the page.
Most assignments in this class will ask you to answer three types of questions:
1: Questions that ask you to write sentences or do derivations. You can either handwrite your answers or type them in.
2: Questions that require you to insert MATLAB code. Make sure that your code is wellcommented. You will reuse multiple codes in other assignments and your project.
Comments will help you understand your code better.
3: Questions that require you to insert a plot. Make sure that your plot does not go over
the boxes provided. Your plots must be well labelled, and the font must be large enough
for the graders to read. Where applicable, insert a legend.
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Section A
Question 1 [5 points]:
Let us start with an “Exact Instructions Challenge!”
You and your friend have been tasked with putting up a lemonade stand at the Purdue
University Fall Fair. Your friend agreed to set up the stand at the Fair location and
you are going to prepare and serve the lemonade. Unfortunately, on the first day of
the Fair you get stuck in traffic and are unable to reach the lemonade stand on time.
You now need to send a complete list of instructions to your friend who is present at
the stand so that they can start preparing and serving lemonade. (Note, use real
lemons not lemonade mix.)
Include as much detail as necessary in each step. Specify deeper than just top level;
don’t just say “squeeze and stir.” Describe how to do that. Your steps should be clear
enough so that your friend is able to prepare and serve lemonade by themselves.
(Emphasis on the lemonade making; they already were tasked with doing the stand.)
Make sure to include all the utensils/ingredients that your friend would need. Write
your answer in the box provided below.
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Answer 1:
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Section B
Question 2 [10 points]:
While on a hike in Turkey Run State Park earlier this summer, you and your lemonade
stand friend found a little creek with a gently flowing stream. You decided to have
some fun by floating a paper boat in the stream. The stream travels at a velocity of
̂ + 0.75𝑡 𝒚
̂ m/s, taking the boat with it at the same velocity as well. [Note: the
v = 2𝑡 𝒙
̂+𝑦𝒚
̂ ]
displacement vector should be of the form x = 𝑥 𝒙
a) What is the velocity of the boat, v, after 𝑡 = 10 seconds?
b) What is the displacement (position), x, of the boat after 𝑡 = 10 seconds? Hint:
Integrate the v equation
c) After 𝑡 = 2𝜋 s, the boat enters an eddy in the stream, and gets a velocity of
̂ + (0.75 sin(𝑡) + 0.75𝜋) 𝒚
̂ m/s immediately. What is
(2 cos(𝑡) + (2𝜋 + 2)) 𝒙
the velocity of the boat at 𝑡 = 4𝜋 seconds?
d) Write a MATLAB code (script) to calculate the displacement and velocity
vectors for the entire duration, i.e., 0 ≤ 𝑡 ≤ 4𝜋.
Make sure your code is well commented and paste it into the box.
Hint: Recall that velocity and displacement are related by 𝑣⃗ =
𝑑𝑥⃗
𝑑𝑡
.
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Answers 2a through 2c:
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Answer 2d: Insert your MATLAB code here
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Section C
Question 3 [8 points]:
Using the code that you generated in Question 2d, plot the following for the duration
the boat stays in the stream, i.e., 0 ≤ 𝑡 ≤ 4𝜋:
a)
b)
c)
d)
̂ direction) of the boat vs time.
Horizontal displacement (in 𝒙
̂ direction) of the boat vs time.
Vertical displacement (in 𝒚
Horizontal velocity vs time.
Vertical velocity vs time.
Hint 1: Remember that upon switching velocities at 𝑡 = 2𝜋 seconds, the boat’s
position does not magically reset to 0; it has moved from the start position. Start the
second set of calculations from the new initial position.
Hint 2: Use MATLAB subplots and turn “grid on.” These will improve the look and
feel of your presentation. You can save plots as separate image files and paste them
into your submission documents. Use thicker plots lines to improve visibility, and
ALWAYS label your axes and title of the plot(s).
Hint 3: Typically, your submissions need to be a single PDF document. Learn how to
merge or combine multiple PDF files into one, how to edit and move pages, etc. Look
for a PDF editor online. Free tools exist.
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Answer 3: Insert plot here
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