Application of a Hyperbola

1. Some nuclear power plants utilize"natural draft" cooling towers in the shape of a hyperboloid,a solid obtained by rotating a hyperbola about its conjugateaxis. Suppose that such a cooling tower has a base diameterof 400 feet and the diameter at its narrowest point, 360 feetabove the ground, is 200 feet. If the diameter at the top of thetower is 300 feet, how tall is the tower?

Coast Guard station A is 200 miles directly east of another station B. A ship is sailing on a line parallel to and 50 miles north of the line through A and B. Radio Signals are sent out from A and B at the rate of 980 ft per microsecond. If at 1:00 PM, the signal from 8 reaches the ship 400 microseconds after the signal from A, locate the position of the ship at that time