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Home Continuous Functions How to Set Up a Problem Examples Example 3: Distace between Two Parting Ships (Three Variables depending on Time)
 
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Example 3: Distace between Two Parting Ships (Three Variables depending on Time)

Two ships start at the same point at time t = 0. One ship moves north at 30 miles per hour, while the other ship moves east at 40 miles per hour. Find the distance between the two ships as a function of time.

 

Step 1

The ships start at the origin;

the y-axis points north; and

the x-axis points east.

The diagram is shown in Figure 3.1.3. x and y are the distances of the east- and north-moving ships from the origin, and z is the distance between the ships, all in miles, t is the time in hours.

03_continuous_functions-9.gif

Figure 3.1.3

Step 2

t ≥ 0, y = 30t, x = 40t, z =03_continuous_functions-8.gif

Step 3

03_continuous_functions-10.gif

INTERPRET THE SOLUTION

z = 50t,   t ≥ 0.

t is the independent variable, and x, y, z all depend on t. The distance between the ships is 50t miles, where t is the time in hours.
Home Continuous Functions How to Set Up a Problem Examples Example 3: Distace between Two Parting Ships (Three Variables depending on Time)

Last Update: 2006-11-15