1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

River crossing and relative velocities

  1. Apr 21, 2014 #1
    Hi everyone,

    I've been having difficulties with this problem for a while. Here is my best attempt at solving it. If there's anything wrong, I honestly can't figure it out :). I would appreciate if anyone could go over it quickly and tell me if/what I did wrong.

    1. The problem statement, all variables and given/known data
    A boat crosses a wide river with a speed of 12km/h relative to water. The river has a uniform speed of 6 km/h due east relative to earth.
    (a) Determine the speed of the boat relative to a stationary observer.
    (b) In what direction should the boat be heading to reach an opposite point directly across the river?


    2. Relevant equations
    I've set up the velocities as such:
    Vbe = Velocity of the boat relative to the earth (and observer),
    Vbw = Velocity of the boat relative to the water, and
    Vwe = Velocity of the water relative to the earth.

    Therefore, Vbe = Vbw + Vwe


    3. The attempt at a solution
    After drawing a picture of the situation, I've determined that

    Vbw = (-12sinΘ i + 12cosΘ j) km/h
    Vwe = (6i + 0j) km/h
    Vbe = (0i + Vbe j) km/h ← This is something I'm not certain of. Am I right to assure that since we want to go directly across the river, relative to the earth, this vector should have a 0 i-component?

    Using Vbe = Vbw + Vwe,

    1) -12sinΘ + 6 = 0
    → Θ = 30° (counterclockwise from positive y-axis)

    2) magnitude of Vbe = 12cosΘ = 12cos30 = 10.39

    To answer a) using the above, Vbe = (0i + 10.39j) km/h, or 10.39 km/h due north relative to the observer.
    b) Direction should be 120° from positive x-axis.



    Have I made any mistakes somewhere? For some reason, I had quite a hard time visualizing this problem.

    Thank you for your time!

    Egoyan
     
  2. jcsd
  3. Apr 21, 2014 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Your answer and reasoning look right for b). Part a) is unclear - you cannot answer it without assuming a relative angle.
     
  4. Apr 21, 2014 #3
    Hi,

    Thanks for taking the time to look at the problem.

    That's what I thought too - and that's part of why I had such a hard time visualizing it, I believe. But this was an exam question (I am 100% certain of the phrasing, I've got a copy of it with me), and I was wondering what was the deal here...

    Some of my classmates were illustrating the problem as a triangle, setting it up such that the hypotenuse would be the resultant velocity relative to the observer; that is v=√(12^2+6^2) = 13.4 km/h. Anyone knows if this could be right?

    Thanks again,

    Egoyan
     
  5. Apr 21, 2014 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, I suspect part a should have said "if the boat heads straight across relative to the water". This would make 13.4 correct.
     
  6. Apr 21, 2014 #5
    Ah, yes, I see. Thanks a lot!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: River crossing and relative velocities
Loading...