Math 142 - Calculus II - Fall 2011 – Prof. Janeba             

Project #1


Harold Hadley is very lazy and very rich.  Oh, and he loves to ride his bicycle.  Yes, these may seem contradictory, but there it is.

As Harold rides his bicycle through Salem, he often encounters this problem:  As he rounds a certain bend, he sees a car ahead stopped at a red light.  The car is blocking Harold’s path, so he needs to slow down, but being lazy, he hates to slow down any more than necessary – for then he will have to expend energy to regain his lost speed.

Now the traffic signal timing and Harold’s cycling habits (including speed) are so consistent, that the situation is often precisely this:  His velocity is 20 m.p.h. and he sees the car when his front wheel is 100 feet behind the car’s rear bumper.  Also, these cars seem to accelerate pretty consistently at 7 ft/sec/sec when the light turns green, and the light changes just 3 seconds after Harold sees the car.

You may wonder why Harold doesn’t just get in the habit of coming around this bend at a slower speed, but often the light is green, there is no stopped car, and he need not slow at all.

So Harold is commissioning your consulting team to answer this question:  If he brakes at a constant deceleration starting at the instant that he sees the stopped car, what should that deceleration be so that he doesn’t hit the car but retains as much of his speed as possible?  Oh, and what would happen (give great mathematical detail) if he didn’t brake at all? You should neglect any non-braking deceleration that would occur due to air resistance or other friction.  Granted, these may seem silly questions to invest so much time on, but Harold is rich, and can hire people to do what he wants.  By the way, it’s probably best not to bring up to Harold the vanity of assuming that he can brake at precisely a given deceleration.  Humor him.

Your group, wanting to earn more of Harold’s money in the future, will want to make him happy.  This means that of course you’ll want the answer to be right, and you’ll want to make sure of that by carefully checking, preferably in multiple ways.  [Your grade cannot be higher than a C if the answer is not exactly correct – Prof. J.]  Furthermore, you want to persuade Harold that you weren’t just lucky in finding the right answer, so you’ll need to give a careful report of how you got it.  Harold did take calculus in college, though he’s forgotten many of the concepts, and will need some reminding.  He’s still good at algebraic calculation, though.  So you’ll want to write up a detailed report explaining how you set up the problem, why your setup is correct, and how you solved it.  Algebraic simplification doesn’t need lots of explanation, but you will need to give enough detail that Harold can reproduce your calculations without any guessing on his part.  You’ll also want to look at the overall question and situation, describe just exactly what your solution will accomplish, and see if you can offer some tactful advice to Harold that he might appreciate.  [This is how you earn a grade higher than a C.]

Consulting firms will be required to make a private group presentation of preliminary results to Mr. Hadley’s consultant evaluator, Prof. Janeba, on either Wed. Sept. 7, or Thurs. Sept. 8.  Please make an appointment with Prof. Janeba - there are limited appointments available on each day.  Come to your appointment with at least a fairly detailed plan for finding the solution, if not the solution itself, already worked out and in written form.

Final reports are to be printed on 8.5x11 inch white paper sheets bound with a single staple, submitted to the consultant coordinating office (Ford 216) no later than Tuesday, Sept. 13, at 4:00 p.m...   Be sure that your report is self-contained (in case Mr. Hadley forgets what the question was), and its qualities of completeness, clarity, and correctness reflect your best abilities.  It is perfectly acceptable to write in complex formulas by hand, although groups may find it worthwhile to expend a small effort getting the word processor to type simple formulas and symbols.  NOTE: anything simply shoved under the door after 4 pm that day will be assumed to have been too late!

A Word to the wise: This project is worth about 10% of your course grade.  Please make sure that you are doing the best that you can.  Please carefully read all the instructions and resources provided.

Last Modified August 30, 2011.
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