Hi!
What is happening is not that the end falls to the floor, the spline just stretches a lot.
Put the attribute "Stretch Resistance" on your HairSystem Node to a really high value, for example 10000.
Also you are moving your chain really fast. In dynamics, units are always calculated as meters, so if you move your hand from 0 to 54.4 in 54 frames, that means your hand is moving at a speed of 1m/f -> 24m/s -> 86.7 km/h and it really rapidly accelerates to that speed. This automatically streches your rope during acceleration, so in order to prevent that, you also need to up your attribute "Stretch Damp" by quite a lot (probably also 10000).
This will slow down your playback considerably, but it should eliminate the stretching almost entirely.
But I would consider to switch your work units to meters and make your arm something like 1 long instead of 40. Then you can also use lower numbers in your physics calculations.
Also I would apply a unified squash/stetch to all the joints in the dynamic part of the chain, that allows to let the chain to dynamically squash and stretch without looking weird in the driven mesh.
I hope it helps!
