A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 23 mi/h. Find the speed and direc
1 answer:
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Answer:
23.2 mi/h at N 7.4° W
Step-by-step explanation:
The velocity vectors of the woman and the ship form the legs of a right triangle. The hypotenuse of that triangle is the vector representing the woman's speed relative to the water.
The magnitude of the resultant velocity can be found using the Pythagorean theorem.
r = √(3² +23²) = √538 ≈ 23.2
The given vectors are adjacent and opposite the angle of interest, so the tangent relation applies.
Tan = Opposite/Adjacent
tan(α) = 3/23
α = arctan(3/23) ≈ 7.4°
The woman's speed relative to the water is about 23.2 mi/h. Her direction is about 7.4° west of north.
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