1. A plane is flying at a constant rate of 500 mph at a constant altitude of 1 mile toward a person. a. How fast is the angle of elevation changing when the angle is  /4? b. How fast is the angle of elevation changing when the angle is  /3 Steps for solving related rate problems. 1. Determine the variables that are changing. 2. Determine the rate you want to find. 3. Find a relationship between the variables. This is most often done by using things like the Pythagorean Theorem, Similar Triangles, Trigonometric Relations, and formulas for area, volume, concentration etc. 4. Take the derivative with respect to time before you plug in the values of the variables. 5. Substitute the known values and solve for the unknown you want to find from step 2.  1 mile x  

2. A light house located 1 mile from a straight shoreline. The light beacon rotates a 3 rpm. How fast is the beam of light traveling when it is moving toward the center and making an angle of  /6 with the shoreline? Water is being added to 50 liters of pure acid at a constant rate of ½ liter per minute. How fast is the concentration changing when 50 liters of water have been added to solution? A 6 foot man is walking away from a 24 foot light post at a constant rate of 3 feet/sec. How fast is the length of the man’s shadow increasing when he is 18 feet from the light post? shoreline  /6 A boy is flying a kite and the wind blows it so that the kite flies parallel to the ground at a constant height of 40 feet. If the string is leaving the spool in his hand at a rate of 4 feet/sec when there is 50 feet of sting out how fast is the wind blowing? 

3. A conical tank that is 18 cm high and 3 cm in radius is being filled with water at a constant 2 cm 3 /min. How fast is the height of the water increasing when the water is 6cm high in the tank? 18cm An oil tanker runs into a rock and begins to spill oil in the form of an increasing circular oil slick a uniform ½ inch thick. The hole in the tanker is causing the oil to leak out at a constant rate of 5 ft 3 /min. a) How fast is the radius of the oil slick increasing when the radius is 100 feet? b) How fast is the area the oil slick covers increasing when the radius is 100 feet?