Section 3.9: Related Rates
Guidelines for Solving Related-Rate Problems:
Example: A nugget is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 2 ft/sec. When the radius is 3 feet, at what rate is the total area A of the outer ripple changing?
Example: A nugget is flying on a flight path 3 miles above the ocean that will take it directly over an island. If the distance between the nugget and the island is decreasing at a rate of 200 miles per hour when the distance between them is 5 miles, what is the speed of the nugget?
Example: A nugget is rising at a rate of 15 feet per second when the nugget is 50 feet off the ground. A photographer is standing on the ground 100 feet from the take-off site. If the photographer keeps the nugget in his/her sight, what is the change in the photographer’s angle of elevation when the nugget is 50 feet off the ground?