Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**dvcochran****Guest**

Hello,

I have a boat ramp that if 50 feet long. In the worst recorded floods the water can rise 21 feet. My problem is I need to know the ramp will reduce in length as the water rises in 1 foot increments. I have tried to solve it with various right angle and SSA formulas but cannot figure it out. To start two sides are known; one 50 foot, one 1 foot but I get lost as the one side increases and one side decreases.

I want to learn and understand tne math behind the answer(s) as I have to create a spreadsheet that reflects the results.

Any and all help will be very greatly appreciated.

Best regard,

David Cochran

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,598

Hi;

Welcome to the forum. I do not understand what you mean. The ramp is 50 ft long but what is 1ft? The height of the ramp?

Please specify everything in relation to the drawing below. Left click the drawing to enlarge.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi David,

Welcome to the forum.

We need one additional piece of information. What is the angle of elevation of the ramp?

eg. If the ramp is at 5 degrees then a one foot rise in water level will result in a 1/sin(5) shortening of the dry part of the ramp.

(assuming the ramp rises at a steady rate)

If you don't know this, you'll need to record some data to sort this out.

eg. Observe the water line as the tide comes in. Use local tide figures to get the rise at fixed times and record the corresponding water line position.

It won't be easy to do this accurately*, so a graph of rise in tide height against loss of ramp length will (ideally) give a straight line. Just how well it fits this model will tell you the accuracy of your data.

* For instance, an on shore wind will skew the results.

Model:

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**Calligar****Member**- Registered: 2011-09-24
- Posts: 234

hi dvcochran,

welcome to the forum!

Life isnt a simple Math: there are always other variables. -[unknown]

But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. -Aristotle

Offline

**dvcochran****Member**- Registered: 2012-12-19
- Posts: 2

The ramp is 50 feet long. You could say the ramp starts at 0 degrees angle. I said one side was "one foot" just as a reference point. This is in a river not water with a tide to observe. There is arbitrary rise and fall from the dams being opened and closed but it would be very difficult to map and would not provide any data of value. I need to understand how to start the process from 0 degrees angle and how to convert or show the change in height of one end of the ramp and how much the ramp will shorten as the water rises, ideally in one foot increments. One end of the ramp is fixed and does not move. As the water rises, the other end of the ramp rises (changes angle) and the ramp effectively shortens. These are the main questions I am trying to answer. I have to make a chart that shows the change from 0 feet to 21 feet (the worst recorded flood). I hope this helps.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,598

Hi;

As far as I understand it we should clarify some points. The ramp never really changes in length, but as the water rises the ramp's horizontal distance shortens with respect to the horizontal.

I can make a table of those relative distances.

We have water rise in feet in the first column and the effective length of the ramp is in the second column.

This is my drawing showing the biggest flood of 21 feet. The chart indicates the ramp will only stretch 45.3762 feet across.

The formula that generates the above table is:

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi bobbym,

I'm totally confused. How does this ramp have an angle of 0 degrees.

Is one end fixed, whilst the other floats up and down in the water?

Is that the diagram for your model?

Where did 24 degrees come from?

thanks

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,598

Hi;

One end of the ramp is fixed and does not move. As the water rises, the other end of the ramp rises (changes angle) and the ramp effectively shortens.

He has one end of the ramp fixed and the water raises the other end up. The fixed end acts as the center of a circle.

When the y coordinate is 21 ( 21 ft of water under that end of the ramp ) the ramp makes about a 24 degree angle with the horizontal. This is as much about it as I understand from his question.

The drawing shows how the ramp will look under the worst flood condition ( 21 ft of water ). The table gives the increments for 1 ft of water.

Could all be kaboobly doo if I misunderstood the question!

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,311

hi bobbym and David,

Thanks. I'm still puzzled about how that helps to launch a boat. Essex is on the east coast of England and is very popular with people who own boats. Those who keep their boats at home have a trailer and tow the boat to the water. So there are lots of ramps for launching from a trailer. The ramp slopes down to the water and the owner backs his trailer down the slope until the boat can be floated free. In order to avoid launching the towing vehicle as well (!!) the angle of the slope is critical. You would want the car to be in at most a few inches of water when the boat is in deep enough to float free.

So why is this ramp free to float up and down at one end? And which end? You would need the fixed end to be landwards or you'd have to jump the boat across, and that means the other end is floating at water level rather than submerged, so why does that make a launch easier?

Just curious.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,598

Hi;

Nice shot of a guy launching his truck. James Bond's cars all float so...

I'm still puzzled about how that helps to launch a boat.

From the way he explains it, it sounds more like a drawbridge. I hope the OP comes back before 12 / 21.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**dvcochran****Member**- Registered: 2012-12-19
- Posts: 2

Thanks BobbM,

That is exactl what I needed. I really apprecate your intellect!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,598

Hi dvcochran;

That is exactl what I needed. I really apprecate your intellect!

Oh boy! Now me olde head will double in size and I am already having trouble fitting it through the door.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

Pages: **1**