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Homework Help: Kinematics Book Question -- Rowing a boat across a river at an angle

  1. Dec 9, 2014 #1
    Hi, I was trying to solve the following problem which was assigned to me in my Kinematics course.


    I found this solution for it. I understand the concept of relative velocity of the boat to the flowing river but what I really cannot understand is the trig part, of Vb/r :
    Vb/r = 5cos(theta)i - 5sin(theta)j

    Where did the cos(theta) and sin (theta) come from? I understand that this is represented in vectorial form, but I cannot visualize the direction of this velocity. Probably a graphical solution would solve my problem.

    Thanks in advance
  2. jcsd
  3. Dec 9, 2014 #2


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    What is the "5?" What are the definitions of "sin" and of "cos?"
  4. Dec 9, 2014 #3
    5 is the velocity relative to the 2m/s flow and sin is a function that calculates the fraction out of the hypotenuse value, in this case 5, in a particular direction.

    I can now understand the Vb/r part, but I got confused when I tried to visualise Vb .

    Any help, especially graphical help, would be greatly appreciated.


  5. Dec 9, 2014 #4


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    vb is at 45 degrees because the boat travels 50 m (width of the river) and lands 50 m downstream from A

    Note that the angle between vr and vb is not ##\theta## as I think I read in your drawing....
  6. Dec 9, 2014 #5
    According to the solutions it is not θ' as shown in my diagram, but I do not know of another way to represent it graphically. I simply cannot understand what is going on in the equations.
  7. Dec 9, 2014 #6
    First of all try to understand directions i denotes in the right direction x axis and j to positive y(upwards) hece all ur movements are in y are downwards hence negative j.
    now it makes θ angle with horizontal so cos θ is positive i direction and Sinθ of that vector point downwards it becomes negative j as per their axis so here vb/r represents velocity of boat wrt river (when river is not flowing) to calculate total velocity of body vb u have to add velocity of river vr to it which is -2 (going downwards).
    u do 1 thing reverse j direction downwards and solve eqns again it will give u a more clear idea
  8. Dec 9, 2014 #7
    I understood this part, what I do not understand is vb = vb sin(45)i - vb cos(45)j

    sin(45) = opposite / adjacent = j/i

    therefore, adjacent * sin (45) = opposite, but opposite is supposed to be in the j direction opposing the above equation ..
    Similarly for cos(45) can be seen.. (should be in the i direction)
  9. Dec 10, 2014 #8


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    You have a good point there. Apparently they count the 45 degrees from the point of view of B: angle between line of sight to A and the shore. Somewhat inconsistent compared to ##\theta##. Nothing wrong with that, but they would have done better if they had at least mentioned that choice. Of course it doesn't make a difference because of this particular 45 degree value.
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