Computing output resistance for zener power supply
First find the impedance the base is being driven with.  That's R in parallel with the Zener at the operating point you are using.  You'll need to look in the Zener datasheet.

Next, reflect that impedance to the emitter.  That's the impedance looking into the emitter.  How the impedance is reflected from base to emitter is a function of the gain of the transistor, again, at the operating point it is actually used at.  Put that in parallel with Rs to get the final output impedance at Us.