A patrol boat is powered by a water jet engine, which takes water in at the bow through a $1 \mathrm{ft}$ diameter duct and pumps it out the stern through a 3 in. diameter exhaust jet. If the water is pumped at a rate of $5000 \mathrm{gpm}$, determine

(a) The thrust rating of the engine

(b) The maximum speed of the boat, if the drag coefficient is 0.5 based on an underwater area of $600 \mathrm{ft}^{2}$

(c) The horsepower required to operate the motor (neglecting friction in the motor, pump, and ducts)