Bet You Won't Believe This !

[Ironfish]

Originally Posted by This'nThat

Ironfish,

Welcome to the FORUM.

Uhh ... yeah ... educational so far!

[fatlazyless]

Looking straight down that red line view from the second floor window of Bob Bahre's house on top of Clay Point, the weekly specials posted in the window at Heath's in Centre Harbor are readable with a very cheap telescope.

....wifey to bob.....oh Bob....looks like Heaths has a good truckload special on NY Sirloin....just 1.99/lb.....should be a worth the trip to load up the boat!

[SAUGUS BOATER]

Actually,
Iron fish and Rattlesnake guy's formulas are both incorrect as neither takes into account the refraction constant. While the earths curvature makes the horizon appear slightly higher, the light moving through the earths atmosphere makes the horizon look slightly lower. I am a land surveyor and must make both corrections to every distance I measure (although my instrument makes these calculations so there is no need for tedious formulas !!)

[This'nThat]

Originally Posted by SAUGUS BOATER

Actually,
Iron fish and Rattlesnake guy's formulas are both incorrect as neither takes into account the refraction constant. While the earths curvature makes the horizon appear slightly higher, the light moving through the earths atmosphere makes the horizon look slightly lower. I am a land surveyor and must make both corrections to every distance I measure (although my instrument makes these calculations so there is no need for tedious formulas !!)

They are not incorrect. They are approximations. The complete explanation of the approximations has not been provided. They could be explained -- but I doubt this FORUM is the place to do so.

But it's true that refraction is one of the things left out. Another thing left out is the complete Pythagorean formula. That was done because of the relative difference between the Earth's Diameter (7,900+ miles) and the height (46 feet) of the observers. In addition, the Earth's diameter is not the same at every point on Earth -- so we only used an average. But each of these things have a minor computational effect on the final answer. We're interested in whether the answer is 46 feet or 102 feet -- not whether it's 46 ft or 46.3 ft.

So I think it's a stretch to come in and say "these calculations are incorrect". They're a damn good approximation -- and that's all we're looking for here on the FORUM, I believe.

[jmen24]

Great thread, it is nice to see fellow math geeks showing their stuff.
Makes me wish I had stayed in a field that would have required me to stay current and use what I learned more often, nothing a quick sit down with the physics book wouln't bring back, but you get my point.

Originally Posted by Rattlesnake Guy

The slide rule was one it's death bed when I was in high school. I think America would have been well served to keep it around a bit longer as a teaching aid. You had to have a feeling for what the answer would be to keep the number of decimal points correct. I am sure many of us remember it being illegal to have a calculator in school. I agree that kids need to also know how to use a calculator very well. But they also should need to know how to do it just as well in their heads.

My Calculus Professor in college would still only use the slide rule (when she needed it) to perform her calculations, her statement to us at the beginning of the class was if you intend to use a calculator bring in the manual to tell you how to use it. Very smart person, the funniest thing I remember about her is that while at Princeton she needed a part-time job so she got a job crunching numbers for NASA, it turns out when she was complete they told her she had been doing the hard math to develop the polymer that coats the tiles of the most current style of space craft. It is very impressive to see someone do advanced Calculus out on the chalk board as fast as she could write without slowing down...That board is full slide the next one along, very cool.

Originally Posted by SAMIAM

Two threads in one........I like it!
The other day at Shaws in Laconia,my bill was $16.16........so I gave the girl a $20 bill plus a quarter and a penny so that I'd get a dime back with my change.She got totally flustered and actually called her mgr over to straighten out the register...I was just chuckling to myself......great job in the schools....let them keep using those calculators.

Its funny because I used to get hounded all the time in high school for not showing my work on Algebra calcs, and it wasn't until I phycally did the math infront of my teacher without using the calculator or writing out my math did I receive a pass on having to show the work. The unfortunately thing is not everyone can do that and with "No Child Left Behind", our public schools will not produce the full potential of the students that can, and the ones that can't are even more handicapped when it comes to math.

[JonLevis]

From the helm of my boat, I can see far enough to miss rocks, other boats, people, and most anything else! That is a neat fact...I checked my iPhone and wasn't able to find an App for it! Go Sox!!

[Squam Friend]

How about if only one guy goes up a ladder? I think I remember this to be approximately 4/7 of the square of the distance in miles; giving you the number of feet above the water one person would have to be to see the other at water level. This comes out to 157 feet! That is, (16.6*16.6)*4/7 = 157 feet (rounded). Does that seem right to those of you who have real formulas and not a vague recollection like I have above?

[Mee-n-Mac]

Originally Posted by Squam Friend

How about if only one guy goes up a ladder? I think I remember this to be approximately 4/7 of the square of the distance in miles; giving you the number of feet above the water one person would have to be to see the other at water level. This comes out to 157 feet! That is, (16.6*16.6)*4/7 = 157 feet (rounded). Does that seem right to those of you who have real formulas and not a vague recollection like I have above?

Well I don't recall any of the formulae ( ) so I derived the answers from the trigonometry. I split the difference between the radii given so far and used RG's 16.6 miles for the arc length. I got 45.9 ft for each ladder (the original problem) and 183.7 ft for just one ladder (your question). If the teacher wants, I'll submit my derivation though it's better done with drawings and that may take a bit to do here and now.

EDIT : OK teach, done !

[hazelnut]

My head hurts reading this thread

Never a mathematician here. In my grad class we took a right brain left brain quiz one day. I tested way off the right brain charts!!! Obviously math was never a class that I enjoyed.

[This'nThat]

Originally Posted by Squam Friend

How about if only one guy goes up a ladder? I think I remember this to be approximately 4/7 of the square of the distance in miles; giving you the number of feet above the water one person would have to be to see the other at water level. This comes out to 157 feet! That is, (16.6*16.6)*4/7 = 157 feet (rounded). Does that seem right to those of you who have real formulas and not a vague recollection like I have above?

Actually, this is very simple. See my equation above:

√1.5 X (√Ht1+√Ht2) = d (Statute Miles)(Ht=height in feet).

What happens when there is only one person? Well, set Ht2 = 0 in my equation, and you have your formula for one person!

It turns out that one person would have to have a ladder of 183.7 feet, just like Mee-n-Mac said. Mee-n-Mac, however, obviously likes more complicated formulas. However, my formula is full of simplifiations and approximations -- and Mee-n-Mac's efforts just show that the simplifications are justified -- in this case.

P.S. Mee-n-Mac: Angle CAF is a right angle (it's a tangent). Likewise CM(rB). That's why the simple Pthagorean algorithm works.

P.P.S. Rattlesnake Guy: You're gonna have to get a bigger ladder.

[chipj29]

Help! My brain...it's melting!!

Seriously, you math guys are putting a lot of time into this, and it certainly is very interesting. More than I could do, that's for sure.

[Rattlesnake Guy]

Originally Posted by fatlazyless

Looking straight down that red line view from the second floor window of Bob Bahre's house on top of Clay Point, the weekly specials posted in the window at Heath's in Centre Harbor are readable with a very cheap telescope.

....wifey to bob.....oh Bob....looks like Heaths has a good truckload special on NY Sirloin....just 1.99/lb.....should be a worth the trip to load up the boat!

Les,
You have discovered my original motivation for the thread. Last fall, we were passing "the estate" and I wondered how far down the lake they could actually see the water. We took some photos to try and judge the height above the water. All was going well until I drew a line on the map and realized that you run into an island with this line of sight. That is why I decided to change the premise.

Thanks for all the participation. I was thinking that on the Winnipesaukee forum, even math is lake related.

I picture some poor kid using goggle for his homework and ends up here.

[Coolbreeze]

I read somewhere that Bahre is going to puchase the islands in the way of his view. His intentions are to cut down the trees and demolish the island into big stone fields spread into the lake. All to increase his views down the lake.