To find: The function that models the distance between the ships in terms of time elapsed since their departure.
The function that models distance between ships in terms of time (in hours) is .
Speed of ship sailing south is
Speed of ship sailing east is
Draw the Figure (1) as shown below after time t since departure of ships.
In Figure (1) is starting point of ships, are the points where ship sailing towards south and east reach after time respectively.
Calculate distance and shown in Figure (1) as,
Apply Pythagorean theorem in triangle shown in Figure (1)
Substitute for , for and for in above equation.
Factor from right hand side of the above equation.
Take square root of above equation.
Thus, function that models distance between ships in terms of time (in hours) is .
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