Warm-Up Example Minimization

Airplane and Cessna [6]. A commercial airliner is arriving in Columbus, Ohio, from the south at a speed of 800.0 [km/h]. When the airliner is 600.0 [km] from the Columbus airport, a Cessna aircraft leaves Columbus for the East Coast at a speed of 250.0 [km/h]. When will the minimum distance occur between the airliner and the Cessna Assumption The two aircraft are moving at an angle of 90° to each other. 

At the beginning (t = 0) the distance that separates the airliner and the Cessna is 600.0 [km] (Fig. 11.3a). Then t hours later the location of each plane will be as depicted in Fig. 11.3b. 

As shown in Fig. 11.3b, D represents the distance between both planes at any instant t t 0). According to the Pythagorean theorem, we can write the following equation  

Determine the right procedure to solve the problem. At your level, to obtain the value of t, to minimize the value of D in (11.1), we will use spreadsheets where we have two interesting alternatives to find the value of t to minimize D in (11.1). 

Approximate graphical solution. Plot D (y-axis) against t (x-axis) and, first, visually determine if the function has a minimum or a maximum, whichever is applicable. If the function has a minimum or 

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