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Ferryboat sailing between town

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data

    A ferryboat sails between towns directly opposite each other on a river, moving at speed v_actual relative to the water.
    a) Find an expression for the angle it should head at if the river flows at speed v_river.
    b) What is the significance of your answer if v_river > v_actual?

    3. The attempt at a solution

    a) v_effective = v_actual + v_river
    v_effective = hypotenuse, v_river = opposite, v_actual = adjacent
    Θ = arctan ( v_river/v_effective)

    b) How is it possible for the adjacent to be > than the hypotenuse?
     
  2. jcsd
  3. Jan 18, 2014 #2
    What must the direction of the effective velocity be? What is the direction of the flow? Draw if unsure.
     
  4. Jan 18, 2014 #3
    Untitled.jpg
     
  5. Jan 18, 2014 #4
    If the effective velocity is not at the right angle to the flow velocity, can the ferry serve towns directly opposite each other on a river?
     
  6. Jan 18, 2014 #5
    It can't. v_effective is calculated on the premise of v_river being perpendicular to v_effective. If the position of the town is shifted, the angle between v_actual and v_effective will change and therefore the ratio between v_effective and v_river will change
     
  7. Jan 18, 2014 #6
    The goal of the ferry is to connect the towns. So its effective velocity must be directed "across the river", which means it must be perpendicular to the velocity of the flow.
     
  8. Jan 18, 2014 #7
    In other words, my diagram is valid, isn't it?
     
  9. Jan 18, 2014 #8
    What exactly in your diagram is in agreement with #6?
     
  10. Jan 18, 2014 #9
    You're right. I committed a careless blunder.
    Untitled.jpg
     
  11. Jan 18, 2014 #10
    Can you solve it now?
     
  12. Jan 18, 2014 #11
    I presume this is in response to part (b) and that part (a) is correct.

    As for part(b), I'm not too sure. The question is asking what significance is there if the velocity of the flow is > than the actual velocity. Is it even possible for any of the two lengths in a right angle triangle to be > than the hypotenuse?
     
  13. Jan 18, 2014 #12
    How can part (a) in #1 be correct, if it assumes that the effective velocity is the hypotenuse?
     
  14. Jan 18, 2014 #13
    Θ=arctan(v_river/v_effective)
     
  15. Jan 18, 2014 #14
    Is the effective speed known in advance?
     
  16. Jan 18, 2014 #15
    Nope. It was not given. The questions I posted, as has been, were done so word for word.
    Given the question, I tried solving it symbolically- part(a) can be done so. But part (b) makes no sense to me.
     
  17. Jan 18, 2014 #16
    Try to think logically. Imagine you are the skipper of that ferry. You need to find the angle given what you know. What would you know?
     
  18. Jan 18, 2014 #17
    I do have v_actual, v_effective, v_river and right angle triangle. Is it possible to derive a numerical value in this case?
     
  19. Jan 18, 2014 #18
    Do you have the magnitude of v_effective?
     
  20. Jan 18, 2014 #19
    It was not given.
     
  21. Jan 18, 2014 #20
    I know it was not. You are the skipper, what do you know about your ferry and about your river?
     
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