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Relative Velocity Problem - Finding an angle of a boat going down a river

  1. Oct 2, 2012 #1
    1. The problem statement, all variables and given/known data

    A boat is capable of a constant speed of 4 m/s in a river that is flowing at 2 m/s. If the captain wishes to land 10m downriver while crossing a 50m river, then at what angle should the boat be aimed?

    2. Relevant equations
    [/PLAIN] [Broken]
    Relative Velocity Equation

    3. The attempt at a solution

    He went over this problem after handing our tests back, but this was the last question and he was rushing as class was almost over. This is the information I have:

    B=Boat, S=Shore, R=River

    He found θ by taking tan^-1(10/50) and ended up getting 11.3°. Then he went on to find the x and y components. For the x component, I have written down: V(B/S)x = -V(B/R)x + V(R/S)x -> V(B/S) sin11.3° = -4sinΩ + 2. For the y-component, I have written: V(B/S)y = V(B/R)y + V(R/S)y -> V(B/S) cos 11.3° = 4cosΩ.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 3, 2012 #2
    I'm not sure what is meant by constant speed of 4m/s. Is it in still water or upstream or dowstream or at any certain angle.
    Last edited: Oct 3, 2012
  4. Oct 3, 2012 #3
    This was the exact wording on the test, unfortunately. The way he was explaining it, it seems like the boat was going against the river. So the boat would be going in a westward motion, while the river would be flowing eastward, or vice versa, while the boat was also going "downriver," so I guess that means it is going down 50m and across 10m. Though, there would be no way for us to know this with the information given.
    Last edited: Oct 3, 2012
  5. Oct 4, 2012 #4
    Would love if anyone could help me figure out this problem, thanks.
  6. Oct 4, 2012 #5
    Would probably be best to ask your teacher then, but I think it's meant that the boat's speed is 4 m/s with respect to the ground because there's no other way to determine at what direction the velocity is without stating the exact reference frame. And then the river is also flowing at 2 m/s with respect to the ground.
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