At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west

Question

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t.

Explanation / Answer

let the distance between ships be A A^2=X^2+Y^2 dA/dt=(1/(x^2+y^2))^0.5 *(xdx/dt+ydy/dt) on substituting x and y at 6pm i.e 152,102 we get speed =27.74 knots

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