A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowsprit which is 6 feet above the water. If the cable is hauled in at the rate of 1 foot/second, how fast is the vessel moving through the water when there is 5 fathoms of cable out? What is the acceleration at this time? [Note: 1 fathom = 6 feet]

*Problems in Differential Calculus*, Byerly, 1895

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The answer is: velocity is \(\dfrac{5}{3}\) ft/s, acceleration is \(\dfrac{8}{81}\) ft/s^{2}