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Find the Resulant Vector?
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.
Thanks
1 Answer
- AnthonyLv 77 years agoFavorite Answer
30 degrees North of the horizontal can be 30 degrees North of East or 30 degrees North of West.
Using the analogy of the parallelogram of forces, the resultant vector is the diagonal of the parallelogram formed by sides 8 knots and 2 knots. The angle between the vectors is 90 - 30 = 60 degrees. Use the cosine rule: Note the other angle in the parallelogram is (1/2)*(360 - 60 - 60) = 120 degrees.
a^2 = b^2 + c^2 - 2bccosA
a^2 = 8^2 + 2^2 - 32cos120 = 68 - 32*-0.5 =84
a = 9.165 knots
using the sine rule:
a/sinA = b/sinB
9.165/sin120 = 2/sin theta
10.583 = 2/sin theta
sin theta = 2/10.583 = 0.1890
theta = 10.9 degrees East of North if the current is 30 degrees North of East
or 10.9 degrees West of North if the current is 30 degrees North of West
PS It would be reasonable to leave the answer in the ambiguous form of the question.
The angle would be (90 - 10.9) = 79.1 degrees north of horizontal.