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Homework Help: Relative motion and velocity

  1. Oct 21, 2006 #1
    A fisherman sets out upstream from Metaline Falls on the
    Pend Oreille River in northwestern Washington State. His
    small boat, powered by an outboard motor, travels at a
    constant speed v in still water. The water flows at a lower
    constant speed vw. He has traveled upstream for 2.00 km
    when his ice chest falls out of the boat. He notices that
    the chest is missing only after he has gone upstream for
    another 15.0 minutes. At that point he turns around and
    heads back downstream, all the time traveling at the same
    speed relative to the water. He catches up with the floating
    ice chest just as it is about to go over the falls at his
    starting point. How fast is the river flowing? Solve this
    problem in two ways. (a) First, use the Earth as a reference
    frame. With respect to the Earth, the boat travels upstream
    at speed v - vw and downstream at v + vw. (b) A
    second much simpler and more elegant solution is obtained
    by using the water as the reference frame. This approach
    has important applications in many more complicated
    problems; examples are calculating the motion of
    rockets and satellites and analyzing the scattering of subatomic
    particles from massive targets.​

    I had no problem solving (a), my doubts arise when solving (b).

    I desire to know if the following considerations for (b) are right:
    • When the boat is travelling upstream his speed relative to the water reference frame is v + vw or simply v?
    • When the boat is travelling downstream his velocity relative to the water reference frame is v - vw or simply v?
    • The chest is motionless relative to the water reference frame.

    Thanks in advance for your help. :smile:
    Last edited by a moderator: Oct 21, 2006
  2. jcsd
  3. Oct 21, 2006 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Hi there PPonte,

    I've not been on the forums for a while, but it's nice to 'speak' to you again. All your considerations seem valid to me.

    Edit: My apologies PPonte, I didn't see that your first two statements were actually questions. As SGT says, the velocity of the boat in the water's frame of reference is always v.
    Last edited: Oct 21, 2006
  4. Oct 21, 2006 #3


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    The velocity of the boat relative to the water is v, as is stated in the problem, no matter if the boat is travelling up or downstream.
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