Excel projects in Calculus part 4

If you need background, see my first post:

First Excel in Calculus post.
** If you want the Word and Excel copies, @me (@robebymathdude) on Twitter **

For this forth post, I wanted to focus on the sliding ladder problem that is almost always done when doing related rates.  I used their ID number to generate the length of the ladder and the sliding away from the wall speed.  The students then created several time values, starting from the ladder being vertical through to the near the end where the ladder is almost horizontal. 

The big questions / sticking points with the students on this one were where I asked (#11) for them to describe the pattern.  The fast – slow – fast pattern is pretty easy to see if you solve the problem in general as you get the solution below, and as you are near each extreme, you are dividing by close to zero.  It did lead to some good discussions, especially in class where I solved it in general and then we could talk about the function. 

The other one, that was kinda surprising to me, is #12.  I had expected them to mostly say “change in angle, as y/x is opposite over adjacent” and then we could talk about quotient rule and other things.  But we didn’t even get that far.  Best laid plans and all that……

BTW, contact me privately about the three related jokes in question 13 if you need help.  I just don’t want my students to stumble upon the answer too easily…

**** Instructions:

1. Replace the fake ID number with your own Blinn ID number.  (Pinkish  boxes)
2. Notice that this generates five different numbers for you, in cells B2 through B8.  You will use those numbers in answering the questions. 
3. First, set up and solve the ladder sliding down the wall problem like we did in class, with the length and speed for your ladder the length and speed shown in cells B2 and B3 respectively.
4. Notice that I have five boxes of numbers that are similar in set up.  The t-value or times for you should be thus:
• The first two boxes (starting with cells B12 and B23) should be like mine, 0-1 and 1-2 in steps of 0.1.
• The third box, (cell P1) the time should start with the “halfway time frame” computed in cell B6.
• The forth box (cell P12) the time should start 1 second before the “end time frame” computed in cell B7.
• The fifth box (cell P23) the time should start with the “end time frame” and go until the first time you get a negative value for “length of y”.
5. Your “length of y” values should be computed from the t-value and the values in cells B2 and B3.
6. Your “length of x” values should be computed from the relationship between x and y from the problem you solved in #3
7. A.R.C. means Average Rate of Change, and notice in cell C17 this change is between t=0 and t=0.1.  Compute each of these based upon the numbers in the correct cells.
8. The blueish-grey line in each box is the value of dx/dt computed from the relationship between x and y from the problem you solved in #3
9. The Error in reddish background is the relative error between the “A.R.C. for x” and the computed “dx/dt from the equation on sheet.”
10. “dy/dx numerically” is simply the ARC for y divided by the ARC for x.
11. The “Error of two x rates” numbers seem to follow a general pattern.  Describe the pattern, and offer some explanations (so more than one) about why that pattern would be expected to be observed.
12. Explain and show (so diagrams or equations or the like) what dy/dx represents in the context of this problem in terms of what you covered in precalculus. 
13. The cell with a yellow background is 3 related jokes.  If you can clearly explain all three jokes, you will earn some bonus points.