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Homework Help: Kinematics Problem

  1. Jul 14, 2007 #1
    1. The problem statement, all variables and given/known data
    There are two ships separated by a distance [tex]\gamma[/tex] along a straight coastline. Ship A starts moving perpendicularly to the coastline , and Ship B moves such that its velocity vector always point along the position of Ship A.
    Both ships move at same constant speed. After sufficient time, both the ships will move in a straight line with a constant separation. Find this separation.

    2. MY ATTEMPT

    First, i assumed the constant speed to be v
    and let, after time T, both of them move in a straight line.
    and let [tex]\theta[/tex] be the angle that the velocity vector of ship B makes with that of the other. ([tex]\theta[/tex] is variable from [itex]\pi / 2 \ \rightarrow \ 0 [/itex] ) . I feel [itex]tan\theta \ = \ \frac{\gamma}{vt}[/itex]

    Then [tex]\gamma \ = \ v \ sin \theta \times T [/tex]
    and [tex]x \ = \ T (v-vcos \theta) [/tex]

    x= constant separation when ships are in a straight line

    The problem is, I am unable to get differential equations which i should. How do i convert the known data into differential form ?

    Any help is appreciated
     
    Last edited: Jul 14, 2007
  2. jcsd
  3. Jul 15, 2007 #2
    I don't know a lot about differential equations, but I will say that velocity is the derivative of x(t). If you can figure out the position, maybe you can solve for the T variable. Or perhaps you could work this out like an optimization problem?
     
  4. Jul 16, 2007 #3
    Any means of solving this apart from what I've tried ?
     
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