Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two boats leave shore @ different angles. How long after will they be 800ft apart?

  1. Jun 6, 2006 #1
    Two boats leave the shore at the same time and travel in the directions shown. If [itex]v_A\,=\,20\,\frac{ft}{s}[/itex] and [itex]v_B\,=\,15\,\frac{ft}{s}[/itex], determine the speed of boat A with respect to boat B. How long after leaving the shore will the boats be 800 ft apart?

    http://img366.imageshack.us/img366/8164/engr204problem121995cj.jpg [Broken]

    I figured the relative velocity:







    Here is where I can't figure out how to get the time t for when the boats are 800 ft apart. I try to complete the triangles above and solve for the length of one of the sides and get a wrong answer when I divide by the velocity to get the time since the velocity is constant. Please help!
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jun 6, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You have found the relative velocity, i.e. how fast they are moving apart. How long will it take them to become 800m apart?
    Last edited: Jun 6, 2006
  4. Jun 6, 2006 #3

    It seems the simpler the solution, the tougher it is to find, for me anyways!

    The right answer:

  5. Jun 6, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Looks good to me :smile:
  6. Jun 6, 2006 #5


    User Avatar
    Homework Helper

    The velocity of A relative to B is the apparent velocity A will have for an observer on B. It tells us how object A moves with respect to object B. That is as if object B were stationary how would object A move (with respect to it). So [tex]V_A - V_B[/tex] removes from the velocity of A the part similar to the velocity of B (their relative motion would be zero if they had similar velocities). What is left is the remaining motion of object A w.r.t. object B. So you end up with the velocity of object A with respect to object B, usually indicated as [tex]V_{AB}[/tex].
    Last edited: Jun 7, 2006
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook