At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per h

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Nov 10, 2017

Answer:

#v_{AB} = \sqrt{16^2+21^2} = 26.401 # knots.

Explanation:

#vec v_{AB}# : Velocity of ship A relative to ship B,

#vec v_{AS}# : Velocity of ship A relative to sea,

#vec v_{BS}# : Velocity of ship B relative to sea,

Consider a cartesian coordinate system in which X axis is oriented East and Y axis is oriented North.

#vec v_{AS} = (-16, 0)# knots;

#vec v_{BS} = (0, +21)# knots;

#vec v_{AB} = vec v_{AS} + vec v_{SB} = vec v_{AS} - vec v_{BS}#

#\vec{v}_{AB} = (-16, 0) - (0, 21) = (-16, -21)# knots

#v_{AB} = \sqrt{16^2 + 21^2} = 26.004# knots

"at 4 pm" is just a red herring.

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