SOLUTION: A ship is heading in a direction N 60◦E at a speed which in still water would be 20 km/h. It is carried off course by a current of 8 km/h in a direction of E50s. Calculate the sh

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Question 1200289: A ship is heading in a direction N 60◦E at a speed which in still water would be 20 km/h. It is carried off course by a current of 8 km/h in a direction of E50s. Calculate the ship’s actual speed and direction.
Answer by Alan3354(69443) (Show Source):
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A ship is heading in a direction N 60◦E at a speed which in still water would be 20 km/h. It is carried off course by a current of 8 km/h in a direction of E50s. Calculate the ship’s actual speed and direction.
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Draw a vector OA with its tail at the Origin.
The heading of the boat, vector OA, is 060 degs.
The wind direction is 140 degs.
Draw a vector AB with the tail at A.
The angle OAB is 100 degrees.
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Use the Cosine Law to find the resultant OB.
r^2 = 20^2 + 8^2 - 2*8*20*cos(100)
r^2 = ~ 519.57
r = ~22.79 km/hr
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Use the Sine Law to find angle AOB:
r/sin(100) = 8/sin(AOB)
sin(AOB) = 8*sin(100)/20 = ~0.3939
AOB = ~23.2 degs
bearing = 60 + AOB = 83.2 degs