Final answer:
To calculate the component vectors of the ship's velocity due to sea dragons, current, and wind, trigonometric functions are used. For the sea dragons pulling the ship at 35 mph at an angle 50 degrees north of west, for the current heading southeast at 9 mph, and for the wind blowing at 8 mph at 58 degrees north of east, each of their components along the axes are computed and rounded to four decimal places.
Step-by-step explanation:
To convert the velocities of the sea dragons, the current, and the wind into component vectors, we need to use trigonometry, specifically sine and cosine functions. We are considering the east direction as positive for the x-axis and the north direction as positive for the y-axis.
The sea dragons' velocity can be split into two components using the angle given, 50 degrees north of west. The westward component (negative x-direction) and the northward component (positive y-direction) can be calculated as:
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- x-component: −35 mph * cos(50°) ≈ −27.9556 mph
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- y-component: 35 mph * sin(50°) ≈ 26.7915 mph
For the current going southeast (45 degrees south of east), the components are:
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- x-component: 9 mph * cos(45°) ≈ 6.3639 mph
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- y-component: −9 mph * sin(45°) ≈ −6.3639 mph
Lastly, for the wind blowing at 58 degrees north of east:
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- x-component: 8 mph * cos(58°) ≈ 4.2853 mph
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- y-component: 8 mph * sin(58°) ≈ 6.6982 mph
All components are rounded to four decimal places as requested.