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Find Speed and Direction of yacht with respect to the ocean floor?
A yacht is traveling at a speed of 8 knots per hour due North. The water current of the ocean is 2 knots per hour 30° North of the horizontal. Find the speed and direction of the yacht with respect to the ocean floor. Hint: Find the resultant vector. You must have a drawing.
1 Answer
- CwCcLv 77 years agoFavorite Answer
You don't have to say "knots per hour". A "knot" is already a nautical mile per hour.
All you need to do is add the vectors. If you draw it out, it will probably be easiest to use the tail-to-tip method and do a little geometry with the triangles, but so long as I'm not drawing a picture, I think it would be easier to use components.
8j + 2 cos(30) i + 2 sin(30) j =
sqrt(3) i + 9j =
1.73i + 9j
To get the magnitude of this vector, use the pythagorean theorem.
sqrt(1.73^2 + 9^2) = 9.17 knots
And to get the direction, use an arctangent.
arctan(9/1.73) = 79.1 degrees above horizontal