Two questions

Not puzzles (sorry) but legit questions that I know the minds here will be able to answer.

1) When casting a lure while fishing, is there an optimum amount of line to leave hanging at the end of the rod for the cast? Too little or too much messes up your cast, but somewhere in the middle, it acts like an atl-atl and hurls the lure best.

2) I was giving my class a test, and remarked that I wanted them to achieve the '90% rule' where 90% of them get at least a 90% grade. They didn't quite make it, but I was left with the strange task of trying to calculate just what '% rule' they DID achieve. How to do this?

Compute what percentage of the class ('A' one student is, sort the list of grades, and just take the lowest N*A that's less than the Nth-highest grade.

For example, say there are 8 students whose grades were 72, 72, 81, 88, 96, 68, 57, and 91. 1/8 = 12.5%, so the comparison is:

12.5 96 25.0 91 37.5 88 50.0 81 62.5 72 75.0 72 87.5 68 100.0 57

So 62.5% of the students got at least a 62.5% grade.

If you prefer, you can also do this by making a graph instead of a table. I think the table is easier, and also more suited to computer calculation.

0 works for me, but then I hate fishing.

You could iterate easily enough. This is trivial on a computer.

First, write a function that returns the percentage of students exceeding N%. Then just loop through at whatever granularity you wish, printing a table as you go. You can read off the answer.

works for me, but then I hate fishing.

You could iterate easily enough. This is trivial on a computer.

First, write a function that returns the percentage of students exceeding N%. Then just loop through at whatever granularity you wish, printing a table as you go. You can read off the answer.

[ I see this is crossposted to sci.math, so consider this a first cut, to be improved upon somewhat rapidly by real mathematicians. ]

This is intriguing. If you hate fishing, why do you do it?

I assume that most anglers spend their time sitting on canal banks slowly drowning maggots because it is the only way they know to get away from their families. But I would have expected you to be able to come up with something more creative, and less boring.

<grin> Well, I only go fishing 0 times per year, so it's not too much of a hardship.

I'm afraid I'm even /less/ creative - I do Usenet.

I reckon that the situation would be significantly affected by a number of secondary effects. The stretchiness of the line, the flexibility of the rod, air resistance on the line, etc.

However, if we pose the unrealistic case where all of what are usually minor effects are ignored, the situation starts to look somewhat like a double pendulum. The motion of a double pendulum is chaotic, so I guess that you're unlikely to find an analytical solution.