At noon two boats leave the same dock simultaneously
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
At noon two boats leave the same dock simultaneously. Boat A travels due south at a constant speed of 18 knots, while Boat B travels due west at a constant speed of 24 knots.
(a) Express the distance D (in nautical miles) between the two boats t hours after noon as a function of their individual distances from the dock.
(b) Calculate the rate at which D is changing at 1:30 p.m.
(c) Indicate whether the boats are moving toward each other or away from each other at 1:30 p.m., and interpret your answer in the context of the problem, including units.