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Related rates

  1. Oct 23, 2007 #1
    1. The problem statement, all variables and given/known data

    Ship A travels at 10 knots on a due north course and passes a buoy at 8am. Ship B, travelling on a due east course passes the same buoy at 10am. How fast are the ships separating at 12 am?

    2. Relevant equations



    3. The attempt at a solution

    I'm not familiar with knots and don't know what knots are in km/h. Also, how fast is Ship B traveling then?
     
  2. jcsd
  3. Oct 23, 2007 #2

    HallsofIvy

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    Why would you want to change to km/h? The problem doesn't require that you do. A "knot" is, as the problem implies, a unit of speed (it is one nautical mile per hour but you don't need to know that either to do the problem- just give the answer in knots).

    However, in your second question you hit on the difficulty. You can't possibly answer this without know how fast ship B is traveling and apparently that is not given.
     
  4. Oct 23, 2007 #3
    Would it be possible to find the speed of B by comparing the time it takes for both A and B to pass the buoy?
     
  5. Oct 23, 2007 #4

    stewartcs

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    I don't see how you could. You know nothing of the distanced travelled (which is what you are really after in the first place).
     
  6. Oct 23, 2007 #5
    The time is 4 hours so can't you multiply that by 10 knots to find the distance of A?
     
  7. Oct 23, 2007 #6

    stewartcs

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    Sure, but that won't tell you the speed of B. It will tell you the distance travelled by A which is one part of the problem. If you knew the speed of B, you could take the same approach and find the distance travelled by B (B's speed x 2 hours).

    Then you could use that information to find the rate of change between the two by using the Pythagorean theorem (differentiating it of course).
     
    Last edited: Oct 23, 2007
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