The following group project is to be worked on by no more than three students. You may use any materials you think may be useful in solving the problems but you may not ask anyone for help other than the people you have chosen to work together. This means you may not ask a tutor or any person other than those in your immediate group for help.
You are to type a letter of response to the problem presented backing up your conclusions with mathematical reasoning, formulas, and solutions. Your grade will depend on how well you communicate your response as well as the accuracy of the conclusions.
Note: The Common Final Exam will have one problem of this type as a takehome project in which you will be given the same instructions.
Please sign and date here to indicate that you have read and agree to abide by the above mentioned stipulations.
_________________________________ _________________________
Student Name #1 Date
_________________________________ _________________________
Student Name #2 Date
_________________________________ _________________________
Student Name #3 Date
September 24^{th}, 2001
Mario
Nintendo of America
PO Box 957
Redmond, WA 98073
ChandlerGilbert Community College
ATTN: Calculus Creators
2626 E. Pecos Rd.
Chandler, AZ 85225
Dear Calculus Creators:
It's me…Mario! After enjoying a delicious plate of ravioli, I got a disturbing phone call from my nemesis, Bowser. He had the nerve to call me at home and do a little trash talking (or should I say trash grunting) regarding our big race next month. As you must be aware, we are racing the new Mario Advance Raceway at high noon on October 15  the perfect time for a showdown between me, Mario and that Princess stealing, thorny backed, soon to be a fossil, Bowser! If Bowser only knew about the secret weapon that Luigi and I installed on my new Kart… MAMAMIA, he never would have wasted his foul breath with this trash grunting phone call.
You see, initially my Kart just wasn't performing at a level that would allow me to beat Bowser. Early versions of the new Kart used on the Mario Advance Raceway showed slight problems with the Kart's handling. Thankfully, Luigi and I have ironed out these problems and the crisp, curbhugging handling of the Karts that we have come to expect has finally been accomplished. Not only that, but my new Kart is equipped with "Powerslide" capability. Powerslides are performed by using the "R" trigger button to jump into corners and then simply glide around them using the dpad…MAMAMIA. On certain corners, if I can complete a perfect slide without crashing, I'll receive a slight power boost to reward me. Please keep this proprietary information a secret so that I can surprise Bowser next month! But this is where I need your help. I need a complete mathematical analysis of one of the corners on the raceway where I feel my Powerslide technique will give me a decided advantage over Bowser. Let me explain some of the technical details regarding the race and my new Kart.
We will be racing on the challenging Mario Advance Raceway. Among its many twists and turns, there is a 2.5mile section consisting of a front and backstretch that measure 3300 feet each and a 132footlong turn. See the picture of a previous race for details.
Do you see the tight turn in the upper lefthand corner of the picture…MAMAMIA? That is where I think I can have an edge over Bowser by applying my Powerslide technique and leaving old Bowser in the dust!
During a recent time trial, my pit crew was able to analyze the video from the Nintendo Blimp and measured my distance horizontal (x) distance and my vertical (y) distance every one second as I entered and exited the turn. During this trial, I completed the turn in 12seconds. However, the pit crew and I feel as though I can make the turn within 9seconds. See the attached diagram for details.
I would like to know the vector valued position function of the Kart during this turn with the decrease in time. Please provide a symbolic and graphical representation of this information. Furthermore, prior to taking to the track and attempting the dangerous Powerslide maneuver, I would like to see a simulation of the Kart taking this turn on a computer. In the simulation, does the Kart appear to be taking the turn at a constant speed? Maybe I should say constant velocity? Please explain the distinction between these two terms. Finally, describe the physical relationship between the car's velocity and acceleration. Would I be "feeling" any acceleration during the turn?
Please do a complete writeup of this situation and return to me by October 5, 2001. That should give me plenty of time to analyze your conclusions and get out on the track to practice prior to the big race day!
Anxiously waiting your reply in the pit stop,
Mario
y  axis
x  axis
Checklist for Your Writing Project
Directions:
in.

This list will be used to grade your assignment, and will be returned to you with
comments.
assignment.
Does this paper:

Clearly summarize the problem to be solved?

Provide a paragraph which explains how the problem will be approached?

State the answer in a few complete sentences which stand on their own?

Give a precise and wellorganized explanation of how the answer was found,
including:

algebraic support

graphical support

numerical support
as appropriate?

Clearly label diagrams, tables, graphs, or other visual representations of the
math?

Define all variables, terminology, and notation used?

Clearly state the assumptions which underlie the formulas and theorems, and
explain how each formula or theorem is derived, or where it can be found?

Give acknowledgment where it is due?

Use correct spelling, grammar, and punctuation?

Contain correct mathematics?

Solve the problem(s) that were originally asked?
Instructor Comments:
Your group’s score out of 50 points is _____________.
Scott Adamson and Trey Cox © 2001
