Been following this thread but have not had much to add until now - and that's only my 2cents.
I am totally addiction to puzzles and IQ tests, and can't resists this one either. This one is just some basic high school physics and simple algebra, but the physics has been a while, so bear with me:
You first calculate velocity of the pile driver right before it hits the pile: v2 = u2 + 2as in where u = 0, a = 9.8 m/s2, s = h; v=sqt( 19.61 * H )
The momentum right before impact then is v * P
Since the impact is inelastic, we can say that the pile driver and pile have the same velocity after impact.
Momentum after impact = (P+D)V So, since before impact momentum = after impact momentum, we can say this: v*P = (P+D)V
So V = (v*P)/(P+D)
So the deceleration is: v2 = u2 + 2as in where v = 0, u = V, a = unknown, s = unknown;
The force that retards this movement is: F=MA given F=Unknown, M=P+D, A=unknown see above.
Resistance the sum of both the retardation force and pile-driver plus pile. R = F + P + D in which F is unknown.
I think one needs the R, so one can solve A, so one can solve s.
Maybe I am still mortal, huh? :) Remco