7. In 3001: The Final Odyssey, Arthur C. Clarke writes of a tower that stretches from the Earth's equator to geosynchronous orbit. (a) The hero, Frank Poole, finds himself in the tower and estimates the acceleration of free fall at his altitude to be g/2. Taking into account rotational motion, what is Poole's altitude? (b) Calculate the work necessary to raise a100-kg mass from the surface of the Earth up through the tower to the geosynchronous altitude. Compare your result to he energy expenditure of a rocket that can do the same thingtoday. (Mint. Assume that te rotational correetion is small, and solve iterativelv)