How Does a Pile Driver Work in Terms of Physics?

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The pile driver, with a mass of 150 kg, is dropped from a height of 4 meters, resulting in a potential energy of 5880 joules at the top. Upon impact with the 250 kg pile, conservation of energy principles indicate the mass reaches a velocity of approximately 8.85 m/s just before contact. After the impact, the combined mass of the pile driver and the pile moves with a reduced velocity of about 6.6 m/s. The deceleration of the pile is calculated to be 6.6 m/s², leading to a retarding force of 1650 N acting on the pile. The work done in driving the pile 0.1 m during each cycle is determined to be 165 joules.
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the 150kg mass of the pile driver is dropped 4m vertically and lands, without bouncing, on the end of the pile of mass 250 kg and drives it 0,1m before coming to rest. assume that the retarding force of the pile to motion is constant. find:
a) the potential energy of the mass at the top of the lift by reference to the top of the pile.
b) by applying the concept of conservation of energy the velocity of the mass just before impact with a pile.
c) the velocity of the mass and the pile directly after the impact
d) the deceleration of the pile
e) the retarding force experienced by the pile
f) the work done driving the pile in each driving cycle.
 
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