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anonymous

  • one year ago

A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles. To avoid tropical storm, the captain heads out of San Juan in a direction of 20 degrees off a direct heading to Barbados. The captain maintains the 15 knot speed for 10 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made how long will it be before the ship reaches Barbados if the 15 knot speed is maintained?

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  1. anonymous
    • one year ago
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  2. jim_thompson5910
    • one year ago
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    |dw:1432783836686:dw| S = san juan B = barbados M = middle point of the journey

  3. jim_thompson5910
    • one year ago
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    if the ship is going 15 knots for 10 hours, then how far does the ship travel (assuming it travels in a straight line)?

  4. jim_thompson5910
    • one year ago
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    hint: 1 knot = 1 nautical mile per hour

  5. anonymous
    • one year ago
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    600*15=9000 nautical miles?

  6. anonymous
    • one year ago
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    is that right? or am I misinterpreting?

  7. jim_thompson5910
    • one year ago
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    distance = unknown speed = 15 knots time = 10 hours distance = speed * time

  8. anonymous
    • one year ago
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    OHHH ok so then it would be 150

  9. jim_thompson5910
    • one year ago
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    yeah so the distance from S to M is 150 nautical miles |dw:1432784489817:dw|

  10. jim_thompson5910
    • one year ago
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    what we need is the distance from M to B. We can find that by using the law of cosines

  11. jim_thompson5910
    • one year ago
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    |dw:1432784585295:dw|

  12. jim_thompson5910
    • one year ago
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    c^2 = a^2 + b^2 - 2ab*cos(C) c^2 = 600^2 +150^2 - 2*600*150*cos(20) ... ... ... c = ??

  13. anonymous
    • one year ago
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    okay gimme a sec to calculate

  14. anonymous
    • one year ago
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    I got about 555.92

  15. jim_thompson5910
    • one year ago
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    that's too large

  16. jim_thompson5910
    • one year ago
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    you need to be in degree mode

  17. anonymous
    • one year ago
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    I changed it to degree mode and it's still pretty big, I got about 461.90

  18. jim_thompson5910
    • one year ago
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    better |dw:1432785182237:dw|

  19. jim_thompson5910
    • one year ago
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    then you'll use the law of sines to find angle SMB |dw:1432785226747:dw|

  20. anonymous
    • one year ago
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    so sinA/a=sinB/b=SinC/c right?

  21. jim_thompson5910
    • one year ago
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    yes you'll use that

  22. anonymous
    • one year ago
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    S=20 degrees B= M= s=461.90402 b=150 m=600

  23. anonymous
    • one year ago
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    @jim_thompson5910 are those the right values?

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