My Notes At 8 P.M. an oil tanker traveling west in the ocean at 16 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 7 P.M. while traveling north at 18 kilometers per hour. If the "spot" is represented by the origin, find the location of the oil tanker and the location of the luxury liner t hours after 7 P.M. Then find the distance D between the oil tanker and the luxury liner at that time.D(t) =    At what time were the ships closest together? (Hint: Minimize the distance (or the square of the distance!) between them.)The time is___  :  P.M. (Round down to the nearest minute.)

Question
Asked Oct 27, 2019
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My Notes
 
At 8 P.M. an oil tanker traveling west in the ocean at 16 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 7 P.M. while traveling north at 18 kilometers per hour. If the "spot" is represented by the origin, find the location of the oil tanker and the location of the luxury liner t hours after 7 P.M. Then find the distance D between the oil tanker and the luxury liner at that time.

D(t) = 
 
 
 



At what time were the ships closest together? (Hint: Minimize the distance (or the square of the distance!) between them.)

The time is___  :  P.M. (Round down to the nearest minute.)
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Expert Answer

Step 1

Oil tanker is at the origin at 8 pm travelling west at 16 kmh. So if we assume x axis to be pointed west to east. The oil tanker was 16 km from the origin on the x-axis at 7 pm

 

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Step 2

At t hours after 7pm the coordinates of the oil tanker are:

 

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(16-16,0)

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Step 3

Let y axis be from south to north.

So coordinates o...

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Math

Calculus

Derivative