Another Ghostly Puzzle

GA

Assumes that the 21 cm is measured along the surface of the water, i.e. from the point at which the stem originally breaks the surface.

Otherwise: if the 21 cm is measured from the original position above the water to the position on the surface I think the answer is 22.05 cm.

Assumes that the 21 cm is measured along the surface of the water, i.e. from the point at which the stem originally breaks the surface.

... and also the impossible condition that the stem is rigid and hinged at its base.

What is the diameter of the head? Is the bottom of the head spherical? If not, what?

Too many variables.

When the wind blows, the flower stem will not go in a straight line, it will be in shape of a catenary , the shape defined by the stem stiffness, wind speed and of course water viscosity (visualise plants in strong wind here the additional factor of water viscosity coming in.

Most likely in the end, it will just form a second arc, may be a few mm, where it will bend just a bit extra and dip into water. After all while it is in water it is immune from the wind, so just a portion has to be out of water pummelled by the wind. This portion will form a second catenary.

Of course the wind speed and the head section (in 3 D is necessary, since as it turns, different crossection is exposed to wind.

It is a bit too difficult mathematically for me. I don't know which order of differential equation is required to iterate.

Well if the stem of the flower is stiff and doesn't bend except for at the bottom of the pond and if the head at the base of the stem is the part that touches the water first then the stems length is 27.5 cm and the depth of the water is 17.5 cm. If this is correct then I don't understand why there is any need to know that there are 6 petals on the flower.

the 6-petals are there to throw you off your game and lead you down blind alleys that will only serve to confuse and obfuscate...

1. What constitutes the "head" of this flower.

2. What is the shape of the "head"?

3. To what degree is the head symmetrical?

4. At each of roughly 10 points along the stem, please provide the stiffness in bending.

5. What is the buoyancy distribution of the stem and any other underwater parts?

6. Is "It's" in "It's head has 6 petals..." intended to be "Its"?

7. Is the head of the flower actually part of the flower (the part with petals, stamen, etc) or part of the plant overall? The text seems to indicate that the head is a part of the flower.

8. When you write "it's [its?] head touches the water at a point exactly 21cm from the spot it was before" did you measure along the diagonal from the initial head reference point to its reference point at water contact, or was the horizontal displacement 21cm?

9. What wave action was created by the wind? Should we consider the contact point between water and head to be in a wave trough or at a wave peak?

10. If we simplified the problem to a triangle, the depth of the water and the length of the flower (plant?) would have different values. The question however, says "what is the depth of the water or what is the length of the flower". Does either one or the other get full credit?

11. Can you provide a drawing to clarify some of these issues?

12. When taking these measurements, did you consider using a meter stick to measure the water depth directly? If you did this from a canoe, the boat's effect on pond level would be easier to calculate (and adjust for) than it would be to calculate the plant stem curve as affected by its varying stiffness and buoyancy.

Thank you, Guest, for asking 12 legitimate and pertinent questions. May I be permitted to add to them?

2. What is the shape of the "head"? (2.1) Please provide both plan view and cross sections as required - a conical flower will have different drag than a planar one, and the position of its petals will modify the water contact position. If other than planar, note whether the vertex, edge, or other feature is used as reference position relative to water surface.

(2.A) What bending stiffness do the petals have - the apparent cross-section will be modified by changing shape under wind pressure - and do we need to adjust the "touch" position for the deflection of the petals to a more downwind location? (In other words, did the Original Poster do so when formulating the question!) If "Yes", then (2.A.1) As the petals flutter in the wind, should we use the minimum, average, or maximum deflection? (2.A.2) Similarly, as the flower itself bobs through some range of positions, should we be looking at maximum downwind, minimum downwind, or average downwind location?

(2.B) Do the petals overlap one another through some portion - or the entirety - of their length? While petal stiffness and deflection may be handled by the method of superposition, the drag cannot.

(4.A) What is the cross-section of the stem at each of those positions? Drag will vary with that shape, changing the local force component and therefore the local curvature.

(4.B) Is the stem's cross-section uniform, or changing only in a smooth fashion between those positions?

(4.C) If the stem is any shape other than round, which face is presented to the wind?

(4.D) Does the stem carry hairs, ribs, or other protruberances which may affect local drag? If yes, (4.D.1) What is the shape, size, stiffness, and density or buoyancy of any such hairs or ribs? (4.D.2) What is the distribution of such hairs along the stem (if hairs), or, Do the ribs run parallel to the main axis, or do they spiral?

(5.A) What is the buoyancy of those above-water portions which may become underwater portions when the wind blows? (if ALL of the stem is described, it will not provide an inadvertent additional clue. I'm not trying to sneakily obtain more information than anyone else has available - that wouldn't be fair!)

(12.A) Can we assume that the water volume displaced by the bent stem is negligible compared to the volume of the pond? If not, we may also need to know the average slope of the bank, and the perimeter length, in order to correct the depth.

(13) When will we see the answer and the calculations behind it?

(14) Would all of these issues still exist if we moved the plant into a not-yet-broken bathtub? Reference: http://cr4.globalspec.com/thread/13355

The first-approximation catenary curve(s) will be modified by several of the aspects that you [Guest] have pointed out. I believe that it will be still further changed by the answers to several of my proposed additions.

27.05 cm, same as nickname.

If it is not a plant with 6 petals, but a round plate on top of a stick, when the wind blows, the edge of the plate touches the water, and I am sure that the above calculations are correct. Now, I think that our plate is not round but hexagonal; try to draw the flower with the compass inside the "plate" circle and there will be a "virtual" six sides hexagon (sic). In this case, if the wind blows such that the vortex of the hexagon touches the water, the problem was already solved. What if the wind blows such that the hexagonal plate touches the water with the side (i.e. two vortices are touching in the same time)? Ha?

power...flower...what a generation

The depth of the water is timeless.

The length of the flower is beautiful.

So where is the OP to clear up the missing assumptions from this puzzle? Looks like another dud to me.

I'm not 100% sure of the depth, but the water is COLD!