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Homework Help: Difficult relative velocity question involving boats

  1. Sep 25, 2006 #1
    Here is the question.....Two boats are heading away from shore. Boat 1 heads due north at a speed of 3 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 40° north of east at a speed of 1.7 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.1 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?

    This is confusing me with the numerous relativities.
    I am using the equation V(13)= V(12)+V(23)
    where V(13) is the velocity of object 1 relative to object 3.
    Im not sure how to get this problem started.
  2. jcsd
  3. Sep 25, 2006 #2


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    Draw your vectors.

    [tex]\vec{v}_{P, S} = \vec{v}_{P, B2} + \vec{v}_{B2, S}[/tex]
    [tex]\vec{v}_{B2, S} = \vec{v}_{B2, B1} + \vec{v}_{B1, S}[/tex]
    [tex]\vec{v}_{P, S} = \vec{v}_{P, B2} + \vec{v}_{B2, B1} + \vec{v}_{B1, S}[/tex]

    P - passenger ; S - shore; B1, B2 - boats 1 and 2.
  4. Sep 25, 2006 #3
    Ok, ihave drawn up my vectors and I am trying to plug in my values. I hate to sound stupid, but I'm lost in this process.
  5. Sep 25, 2006 #4
    What's important here is to understand the concept of relative frames. There is always a stationary observer who observes his reference to have zero velocity, if you will, while the other two are either moving towards or away at some rate. You can't just use equations without knowing where they come from.

    So, picture yourself at some intersection where you are pointing north. Some guy on a motorcycle goes away from you. Now there is the guy on the motorcycle who sees you moving south, and now a runner ahead of him crossing the street to some store. Okay, now take a break and figure out what is happening before you try to digest the last piece of information. You see a motorcycle moving away from you, and another man running really fast away from him because he is about to get creamed by traffic. So now, put the last piece in. I'll let you do this yourself and see if you get the idea.

    Just take it slow, and it isn't all that tough. Draw a huge picture so that you can use vector lengths to aid your thought.
  6. Sep 26, 2006 #5


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    You just need to keep on "expanding" the relative formula until you can calculate all the required vectors. When you run into a vector you do not have in terms of given information set up a new formula for its calculation the same way. In the end you need to work your way backwards towards the first formula once you have all the vectors in terms of known vectors.

    Show us how you progress with the problem.
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