SOLUTION: A ship is heading due norhtwest at 15 mph in a river that flows east at 7 mph. What is the magnitude and direction of the ship's velocity relative to the Earth's surface?

Question 114904: A ship is heading due norhtwest at 15 mph in a river that flows east at 7 mph. What is the magnitude and direction of the ship's velocity relative to the Earth's surface?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A ship is heading due northwest at 15 mph in a river that flows east at 7 mph. What is the magnitude and direction of the ship's velocity relative to the Earth's surface?
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Draw the picture on a coordinate system.
The ship vector is heading 135 degrees with magnitude 15
The water vector is heading east with magnitude 7.
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The resultant vector is:
x-coordinate: 15cos(135)+7cos(0) = -3.6066...
y-coordinate: 15sin(135)+7sin(0) = 10.6066
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magnitude = sqrt(-3.6066^2 + 10.6066^2)= 9.9746 mph
direction = arctan(10.6066/-3.6066)=108.78 degrees
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Cheers,
Stan H.

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