FYKOS Year 33 Series 3 Problem 3 — umbrella · FYKOS 33 #33.3.3
Physics · mechanics · thermodynamics
Problem
As you probably have noticed, water flow creates a mushroom-like shape when a teaspoon is placed against it (e.g. while washing the dishes).
Assume (for simplification) planar round-shaped teaspoon of small radius. When placed perpendicularly to the flow,
falling from rest from the height h,
a wonderful rotational paraboloid would form. Find the optimal height to put the teaspoon in to maximalise the distance from the original flow axis to the place, where the falling water touches the surface (e.g. of the sink). Assume water to be an ideal liquid (uncompressible, zero viscosity, no inner friction).
Bonus Find optimal height to maximalise the volume of the paraboloid.