please help with this

Question

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

Answer 2

N

W E

S

At noon:

A ----- 20 n mi ------ B

At 3 pm:

..............................................................................................B

................................................................................./............ |

..................................................................../......................... |

.............................z........................../.................................... |

........................................./....................................................|

................................/................................................ y=24*3 = 72 n miles

........................./.................................................................... |

................../.......................................................................... |

........./.................................................................................... |

..../......................................................................................... |

A --------------x = 20 + 18*3 = 74 n miles ------------------------C

z² = x² + y², or deriving we get 2 z z' = 2 x x' + 2 y y' or simplifying we get

z z' = x x' + y y'

z = sqrt(74² + 72²) and so z' = (74*18+72*24)/sqrt(74²+72²) = 29.64 knots