Section 3.4

Here are the steps to follow in solving a Related Rates problem:
1) Draw a picture.  Make sure to label quantities that are varying with variables and quantities that are not varying with constants.

2) Write your "let statements" in sufficient detail so as to completely describe your variables.  Include the proper unit.  Time will always be one of your variables.

3) Write down the derivative(s) you are given and the derivative you are being asked to find.

4) Write an equation that relates the variables found in the numerators of your derivatives.

5) Differentiate both sides of the equation with respect to time.

6) Substitute in values for all unknowns except the derivative you are asked to find.

7) Solve algebraically for the unknown derivative.

8) Answer the word problem in words, making sure to include the proper unit on your answer.

Note: Steps 6 and 7 may be interchanged.


Here are the three problems I worked out in class as examples:
1)  A ladder 20 ft. long leans against a wall.  If the bottom of the ladder slides away from the building along the ground at a rate of 2 ft./sec., how fast is the ladder sliding down the building when the top of the ladder is 12 ft. above the ground?

2)  A television camera is located at a point 3000 ft. from the base of a rocket launching pad.  Assume the rocket rises vertically and the camera elevation angle increases in such a way as to keep the camera trained on the rocket.  If the rocket is rising vertically at 880 ft./sec. when it is 4000 ft. up, how fast must the camera elevation angle change at that instant to keep the rocket in sight?

3)  A conical water tank with vertex down has a radius of 6 ft. at the top and a height of 12 ft.  If water is being pumped into the tank at a rate of 10 cubic ft./min., how fast is the water level rising when it is 3 ft. deep?