Conservation of Energy?!?

Question

I'm having difficulty with my physics homework. If anyone can help me... please do so. Heres one of the questions:

A pile driver is a device used to drive stakes into the ground. While building a fence, Adam drops a pile driver of mass 3000 kg through a height of 8.0 m. The pile driver is opposed b a resisting force of 5.0 x 10^6 N. How far is the stake driven into the ground on the first stroke???

I know the formulas : Work = (mass) (gravity)(height) and
Work= Force (distance) (cos theta)

please HELP ME!

Answer 1

First, compute the kinetic energy of the pile driver:
It hass mass of 3000kg and travels the 8 meters plus the displacement of the stake, let's call that d

E=m*g*(8+d)

all of this energy will be transferred into the stake by doing work against the opposing force of 5X10^6 N
this force will do work against the pile driver as:
F*d
So F*d=m*g*(8+d)
d(F-m*g)=m*g*8
d=m*g*8/(F-m*g)
d=3000*9.81*8/(5x10^6-3000*9.81)
d=0.047m