At noon, Boat P leaves a pier and travels due south at a constant speed of 12 km/h
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
At noon, Boat P leaves a pier and travels due south at a constant speed of 12 km/h. Boat Q is located 9 km east of the pier at 12:20 p.m. and begins to sail due west at a constant speed of 15 km/h.
Time t is measured in hours after noon.
(1) Part 1: (a) Using a coordinate system with origin at the pier, x-axis pointing east, and y-axis pointing north, write expressions for the position of each boat for t≥31 h (12:20 p.m.).
(2) Part 2: (b) Compute the distance between the two boats at 12:40 p.m.
(3) Part 3: (c) Determine the rate at which the distance between the boats is changing at 12:40 p.m. State the value with the correct sign and units.