Filling a bottle of water

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

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