Posted by **Anonymous** on Monday, October 26, 2009 at 11:34am.

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 4 PM?

- calculus -
**MathMate**, Monday, October 26, 2009 at 12:00pm
At noon, t=0, A is at (0,0), and B is at (10,0).

A goes due west at 18 knots, and B due north at 22 knots.

The relative velocity vector of B relative to A is **Vb**-**Va**=(18,22)

The distance D in nautical miles in terms of time, t hours after noon, between the two ships is expressed by the function:

D(t)=sqrt((10+18t)² + (22t)²)

Thus the rate of change of distance is given by the derivative:

D'(t) = (404t+90)/sqrt(202t^2+90t+25)

and at 4 pm, t=4, and

D'(4) = 28 knots approx.

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