Calculus I MATH 131 Fall 2025

A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow.

If the rope is being pulled in at a rate of 2 feet per second, how fast is the boat approaching the dock when the length of rope from bow to pulley is 13 feet?

A swimming pool is \(60\) feet long and \(25\) feet wide. Its depth varies uniformly from \(3\) feet at the shallow end to \(15\) feet at the deep end, as shown in the Figure 2.

Suppose the pool has been emptied and is now being filled with water at a rate of \(800\) cubic feet per minute. At what rate is the depth of water (measured at the deepest point of the pool) increasing when it is \(5\) feet deep at that end? Over time, describe how the depth of the water will increase: at an increasing rate, at a decreasing rate, or at a constant rate. Explain.