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Math Help - Relative Velocity Question

  1. #1
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    Relative Velocity Question

    I can't figure out the last two parts of this question.

    A power boat has cruising speed of 60 km/hr. It is taking part in a race around three buoys arranged in an equilatral triangle. The second buoy, B, is 5 km due East of the starting/finishing buoy, A. The third buoy, C, is to the North of the line joining A and B. There is a current flowing at 10km/hr from the south-west. In what direction should the boat be steered on each leg of the race and how long will it take the boat to complete one circuit?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by favorit View Post
    I can't figure out the last two parts of this question.

    A power boat has cruising speed of 60 km/hr. It is taking part in a race around three buoys arranged in an equilatral triangle. The second buoy, B, is 5 km due East of the starting/finishing buoy, A. The third buoy, C, is to the North of the line joining A and B. There is a current flowing at 10km/hr from the south-west. In what direction should the boat be steered on each leg of the race and how long will it take the boat to complete one circuit?
    Draw pictures of the three velocity triangles. Lable know angles and sides of velocity triangles. Solve for the remaining angles and sides.

    Turn the appropriate angles into a headings. The speed on a leg is the appropriate side of the velocity triangle for that leg. Turn the speeds on each of the legs into a time and sum.

    Report back any specific problems.

    CB
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  3. #3
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    Thanks for the reply! I end up going around in circles after I draw the B-C velocity vector triangle.

    I end up with 3 sides: Vb (velocity of the boat): -ucos60i + usin60j
    Vc (velocity of the current): 5√2i + 5√2j
    Vb/c (velocity of the boat relative to the current) : -60cosθi + 60sinθj

    and another angle alpha. I cant find an eqution in which either only the velocity (u) or theta are present, I keep ending up with both of them in an equation which I cant solve.

    I think I've uploaded the diagram I've drawn, its bad i know.
    Attached Thumbnails Attached Thumbnails Relative Velocity Question-relative-velocity.jpg  
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  4. #4
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    wow I had the exact same question in my applied math homework assignment. By any chance do you go to nuigalway?
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  5. #5
    Newbie TheDrBraniac's Avatar
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    Question So what is the answer?

    So, at the end of the day; what is the answer? I got 16.5 minutes.
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