Within the middle of my garden pond is a water-lily, the base of the flower head is exactly 200mm above the pond water. If I pull the flower towards me, when the base of the flower head sinks to the level of the pond water, I notice that the distance between the original location of the flower stem, to where I have pulled it, is exactly 600mm – how deep is my garden pond?

For clarity, below is a dimensioned diagram of the above problem (not to scale).

As ever, along with your answer – show your working.

 

hi Hymie.
Is this homework.?
E

 

hi Hymie.
Is this homework.?
E

No- it’s to exercise your mind – and find out how deep my pond is.

 

800 mm
Pythagorean theorem.

 

800 mm
Pythagorean theorem.

That was too easy – I was given another more complex method to arrive at the answer; I’ll modify the question such that it is not so simple.

 

Ever windsurf? Your question brought back to me something I worked on decades ago.

When you get on the board and need to pull the sail up, it can be quite difficult. With no wind and if you have decent balance, it's not too bad. But in a strong wind with waves it can be nearly impossible.

Anyway, I had an idea for away to make it easier and worked out the physics of the tension needed versus the positioning of the various components. The calculations were far more challenging that one would imagine. Never got around to actually making the product.

The kid in the picture is suffering from his low angle of attack. He's pulling mightily on the rope (called the uphaul) but I think you can appreciate that the majority of his tension is pulling against (parallel to) the mast instead of lifting it (perpendicularly) up and out of the water. If he would stand up even a little, the tension would be greatly reduced.

 

Use Stanley's rule- and some waders!

 

Within the middle of my garden pond is a water-lily, the base of the flower head is exactly 200mm above the pond water. If I pull the flower towards me, when the base of the flower head sinks to the level of the pond water, I notice that the distance between the original location of the flower stem, to where I have pulled it, is exactly 600mm – how deep is my garden pond?

For clarity, below is a dimensioned diagram of the above problem (not to scale).

As ever, along with your answer – show your working.

View attachment 153178

I do not think this question is for an electronics forum.

 

I do not think this question is for an electronics forum.

Which could be why it was posted in the Math forum.

 

Which could be why it was posted in the Math forum.

Sorry about that, I did not knew you had a math forum.