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Snell's law problem about the angle of a wave and the coast

  1. Jul 16, 2015 #1
    1. The problem statement, all variables and given/known data
    First question:
    The waves are approaching at an bearing of N70W, and at N50W, to a coast with a N13ºE orientation. What is the angle of the wave offshore?
    Answer: 7 degrees and 27 degrees.

    Second question:
    The wave is approaching at an angle of 135º. The coast is at 305º. What is the angle of the wave offshore?
    Answer: 80 degrees.

    Third question (now the total confusion):
    The beach is facing north-south. The wave is approaching at an angle of 277º, and 230º. What is the angle of the wave offshore?
    Answers: 7º and 40º.

    Fourth question:
    The wave is breaking in a coast with a East-West orientation, having a N10E bearing. What is the breaking angle?
    Answer: 10º.

    Fifth question:
    What is the incidence angle on open waters of a wave with a bearing of 130º, in a coast with a direction of 80º?

    2. Relevant equations

    This is the formula we used at class:
    Velocity of the wave offshore (as it is coming from the ocean) / Velocity of the wave when it is breaking = Sine of the angle of the wave offshore (as it is coming from the ocean) / Sine of the angle of the wave when it is breaking
    3. The attempt at a solution

    First question:
    Here's how I THINK the answer could have been achieved. I am just to convert the N70W to azimuth; it becomes 290, then I subtract 90 degrees until I get to a angle that is within 90º of the other one. Then I can subtract, that is, 20-13=7. But I do not know if this is the right method.

    Second question:
    My thinking: 305-90= 215 ; 215-135=80

    Third question:
    I don't know. If I use the above method, it works for the first angle, but the second angle would give me 50 degrees instead.

    Fourth question:
    This one seems straightforward but I am not going to assume anything!

    Fifth question:
    I don't know neither the answer nor how it is supposed to be done.

    My teacher talked something about a projection, is it a orthogonal projection or...? He also talked something about drawing a perpendicular to a coast?
    I can't find anything on the web that is similar so I can figure it out. PLEASE help. If someone could give me the name of this kind of exercise, and some explained examples, I could try, but I haven't found much after hours of searching.

    I have tried solving this, but I don't know if I am right or not.

    I've been pulling my hairs for these ones! I have spent many a good hours on this, almost the entire day actually. If it didn't come through as I wrote the post, note the time here in Portugal is 4:30 AM. :(

    Sorry if the wording seems odd, as I have translated it from Portuguese.

    Thanks very much.
     
  2. jcsd
  3. Jul 17, 2015 #2
    Seems like some careful diagrams would help.
     
  4. Jul 17, 2015 #3
    I made a diagram for one of the cases, I'll make some more, but am I on the right track so far? I haven't got much of a clue to be honest with you.

    SEE DIAGRAM IN ATTACHMENT.

    Seeing it a little different now than I was at the OP, I first drew the beach at the orientation given. (I drew it through the other quadrant as well, since the beach is not in just one quadrant right?). Then I drew the wave. Then I drew a perpendicular of the beach: this is what I don't know the reasoning behind, but I remember we did something like this in class. Explanation please? Then I just measured from one angle to the other one.

    Tried to make it somewhat clean for educational purposes, maybe someone else will have this question one day. :D
     

    Attached Files:

    Last edited: Jul 17, 2015
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