SUMMER HOMEWORK PROBLEMS

Problem #1 (August 8th, 2018)

It's a weird day for Mr W: The FRESHMAN force is pulling very hard on him in the Freshman direction.

Meanwhile the INNOVATION force is pulling equally hard on Mr W in the (opposite) APC direction.

  1. Please do a sketch that shows the vectors of each force pulling on Mr W.
  2. The length of your vectors should indicate the magnitude of each force
  3. The direction of your vectors should indicate the direction of each force

═══════════════════════════

The freshmen force can be mathematically represented as follows:

(whining)(cajoling)/(resignation)

The innovation force can be mathematically represented as follows:

(working)(struggling)/(grit)

  1. Please write a mathematical equation that shows those two forces as they work on Mr W's sanity.

  2. Now please derive an equation that shows all of those component parts as a function of grit.

The good news is you can (and should) communicate with other folks in our class.

The bad news is you CANNOT communicate with me or any other non-APC-Classmate on this problem. At all... For any reason...

If you're already trying to google this, shame on you...

When you have a working solution to the problem and you have appropriately addressed each question (in writing please), please mark the appropriate box on our summer checklist page with an "x"

═══════════════════════════

Problem #2 (August 8th, 2018)

Consider the following graph:

      1. Please determine an equation for that graph based on what you see there. DO NOT LOOK IT UP... Figure IT OUT (for this part of the problem assume x and y axis as per usual)

      2. Now please remember back to your dim dark days of kindergarten and recollect a nursery rhyme that has jumping cows and the moon as the main characters

      3. Now let's say that we are trying to determine the best way to analyze this data in a way that BEST fits with our nursery rhyme (hint: one line in particular works) ((hint hint: notice the axis labels) AND provides us mathematical data.

      4. Please suggest how you would use calculus to determine useful information relating to that nursery rhyme using that graph, and only that graph

The good news is you can (and should) communicate with other folks in our class.

The bad news is you CANNOT communicate with me or any other non-APC-Classmate on this problem. At all... For any reason...

If you're already trying to google this, shame on you...

When you have a working solution to the problem and you have appropriately addressed each question (in writing please), please mark the appropriate box on our summer checklist page with an "x"

═══════════════════════════

Problem #3 (August 8th, 2018)

Back in the 1910's and 20's, physics underwent some astounding changes as "Newtonian Physics", often referred to as "classical physics" quickly found itself outdistanced by Relativity and Quantum Mechanics and other innovations that we frequently refer to as "modern physics".

One of the giants of that time was a New Zealand born physicist names Ernest Rutherford (he was very famous for having his graduate students do mountains of research, data collection and analysis, and then happily jumping in at the end and taking all the credit -- but I digress).

Working in London, and as a citizen of the then British Empire he was showered with titles and such and became known 'officially' as:

1st Baron Rutherford of Nelson, OM , FRS HFRSE LLD which stands for:

 1st Baron Rutherford of Nelson, Order of Merit, Fellow of the Royal Society, Honorary Fellow of the Royal Society of England, Legum Doctor (Doctor of Laws)... but I digress (again)

One of my alltime favorite sayings is attributed to 1st Baron Rutherford and it reads thusly:

"All science is either physics or stamp collecting"

Now... consider the following graph in light of that quote:

      1. Why did I have you go through all the work of reading that background on Rutherford? (Think AP Test)

      2. Please determine an equation for that graph based on what you see there. DO NOT LOOK IT UP... FIGURE IT OUT (for this part of the problem assume x and y axis as per usual)
      3. Let's say we want to quantify just how accurate Rutherford's famous quote works for us individually. Please suggest a method using calculus to obtain numeric data from that graph (and ONLY from that graph) that best allows us to utilize that data in the manner described.

The good news is you can (and should) communicate with other folks in our class.

The bad news is you CANNOT communicate with me or any other non-APC-Classmate on this problem. At all... For any reason...

Oddly enough there is method to my madness here, please take it seriously.

If you're already trying to google this, shame on you...

When you have a working solution to the problem and you have appropriately addressed each question (in writing please), please mark the appropriate box on our summer checklist page with an "x"

═══════════════════════════

HINT: This would be a MOST excellent time to get in the habit of meeting a small group of your classmates down at Java & Clay for a 16 oz, white chocolate mocha (in a mug) and thrashing through the problems together.

HINT HINT: I'm quite serious about that.