A nursety rhyme goes "Humpty Dumpty sat on a wall, Humpty Dumpty had a great fall. All the king's horses and all the king's men couldn't put Humpty Dumpty together again."

(a) Describe the energy of the Earth-HD system before, during (including the instant just before impact), and after the fall. Use bar diagrams showing \(K\), \(U, E_{\mathrm{s}}\), and \(E_{\mathrm{\tau h}}\) to illustrate your description.

(b) In terms of the energy of the Earth-HD system, explain why all the king's horses and all the king's men could not put HD together again.

(c) Now assume that things had turned out differently for HD. The king's men were able to set up a net so that he fell into the net and bounced back up and once again sat on the wall. Draw energy bar diagrams for this situation, showing the distribution of energy during the fall, at the instant HD arrives at the net (choose the instant at which the net with \(\mathrm{HD}\) in it is stretched to the lowest position), during the ascent, and when he is back sitting on the wall.