Re: Filling a bottle of water

On Jul 30, 12:31 am, RCA <rcan...@xxxxxxxxx> wrote:
This is a problem I have run into:

I am trying to fill a bottle at the water fountain. My goal is to fill
as much water as possible given that I cannot get the bottle to come
completely under the fountain. Here is a simplified statement of the
problem. Assume that the water fountain is a perfect horizontal disk
of radius R = 15 cm with negligible thickness. Also, assume that the
water comes out of a tap at the edge of the disk at a uniform
horizontal velocity such that the water reaches a maximum height H = 5
cm. Also, the distance that the water falls at along the disk is 20 cm
from the tap. Now, assume that the bottle is a perfect cylinder of
height HBottle = 30 cm and mouth radius RBottle=5 cm.

The question is, where should I position the bottle along the rim, and
at what angle to the vertical, horizontal x and y axes, so that I can
get maximum water in one filling? Given that the bottle is taller than
the maximum height, I cannot place it to fill it completely.

Thanks
Anand

Sorry, one correction - the mouth diameter is 5 cm, not its radius.
Also, assume that the water flows from the edge in a parabola, that is
(in the horizontal plane) exactly along the diameter of the water
fountain disk.

.

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