Page 72 - Calc for the Clueless

The unknown landing point P is x miles from C, the closest point. We get IP by the Pythagorean theorem.
Since CH is 12, PH is 12 - x. We need to set up an equation for time, where time = distance/speed.

Distance Speed

2
2
from I to P (water) (x + 16) 1/2 3 (x + 16) 1/2 /3
from P to H (land) 12-x 5 (12 - x)/5

Let us now tackle other kinds of word problems, which should be a little easier.

Related Rates

The rates we will talk about refer to how things change with respect to time. Related rates are how the rates of
two or more variables are connected with each other.

Before we try some problems, we will give an equation and differentiate it with respect to time. Suppose we are
given

Example 16—

x, y, and z are variables and all are functions of time. What we will do is differentiate the equation implicitly
with respect to time. How does this differ from before?

2
2
When we were given y = (x + 1) 100 , we let u = x + 1, and

so