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At noon, ship a is 40 nautical miles due west of ship b. ship a is sailing west at 18 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)

Answer :

The distance between the ships changing at 92.29 Knots

  • Using the position of ship A as the reference point, at time t measured in hours past noon, ship A is 18 t miles west of this point and ship B is 40 + 17t north of this point.
  • The distance between ships is then

                              [tex]d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\[/tex]

The rate of change of distance is -

                              [tex]\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }[/tex]

after putting t = 5 into this rate of change ,

we get, answer = 92.29

To learn more about differentiation from the given link

https://brainly.com/question/25081524

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