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Homework Help: Sudmarine sonar/distance problem

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data
    A submarine pings its sonar and 9 seconds later hears an echo, the signature of which indicates a battleship. Ten seconds later, the ping takes 8 seconds to echo back. The submarine is traveling at 10 m/s towards the battleship. The battleship is directly in front of the submarine, traveling at the same bearing, at an unknown speed. The salt water is at a temp of 20 degrees C. How long until the sub is directly below the battleship, assuming no change in course or speed in either vessel? What is the speed of the battleship?

    2. Relevant equations
    Sound travels in the salt water at 1533 m/s at 20 degrees C.
    V= d/t
    I am sure there are more but that is what i used

    3. The attempt at a solution
    1.) v=d/t
    1533 = d/8
    d = 1533 * 8
    d = 12264 m

    v = d/t

    10 m/s = 12264 m/t
    t = 12264 / 10
    t = 1226.4 seconds time for the sub to reach the battleship

    3.) v=d/t
    v = 12,264 m / 1226.4 s

    v= 10 m/s for the battleship speed which this is where i am getting hung up on i don't believe this is right cause it has the same velocity as the sub. Any help would be appreciated thank you.
  2. jcsd
  3. Jan 22, 2009 #2


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    Homework Helper

    Keep in mind that both ships are in motion during the time the ping emits to when it is detected.

    Hence the distance the ping travels is the distance between the 2 plus the distance the battleship moved until pinged and then the distance covered back to the sub by the echo is diminished by the distance the sub has traveled until reception.
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