## Related Rates Introduction

The following is a Related Rates problem:

An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna. When the plane is 10 miles away, the radar detects that the distance S is changing at a rate of 240 miles per hour. What is the speed of the plane?

I. Identify what is Given and what it is that you have to Find, verbally.
II. Structure the information, using a diagram.

III. Identify the variables and the constants.
a) The altitude is constant, noted on the diagram as V = 5 miles
b) There are 2 variables that are parts of the diagram:
H the horizontal distance from directly above the Radar at point A to the plane at point B
S the diagonal distance from the Radar at point O to the plane at point B
c) There are 2 other variables that relate to time. What are they and how in this calculus course do we represent them?
______ the rate of change of S with respect to time
______ the rate of change of H with respect to time
Which of these represents the speed of the plane?

IV. Write the equation that represents the diagram.
V. Differentiate the equation.
VI. Substitute to find the solution to the problem.