Problem 15.2. A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1′ = "one minute" = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.

(a) Find the length of one nautical mile to the nearest 10 feet.

(b) A vessel which travels one nautical mile in one hours time is said to have the speed of one knot; this is the usual navigational measure of speed. If a vessel is traveling 26 knots, what is the speed in mph (miles per hour)?

(c) If a vessel is traveling 18 mph, what is the speed in knots?