a ship travels 18mph at a bearing of S30°W write the velocity vector in terms of i and j

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eliberty518 eliberty518

11-04-2024
Mathematics

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a ship travels 18mph at a bearing of S30°W write the velocity vector in terms of i and j

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wait2 wait2 · Answer 1 · 2024-04-11T23:48:20+02:00

To express the velocity vector in terms of its horizontal (i) and vertical (j) components, we need to break down the velocity into its northward and westward components.The bearing S30°W means the ship is traveling 30° westward from due south. Since south is directly downward on a coordinate plane, the westward component is negative.We can use trigonometric functions to find the components:The northward component (i) is given by the formula: velocity * cos(angle) The westward component (j) is given by the formula: velocity * sin(angle)Given: Velocity = 18 mph Angle = 30°Using trigonometric functions:Northward component (i) = 18 * cos(30°) Westward component (j) = -18 * sin(30°) (since it's westward, it's negative)Now, let's compute these:Northward component (i) = 18 * cos(30°) ≈ 18 * 0.866 ≈ 15.594 mph Westward component (j) = -18 * sin(30°) ≈ -18 * 0.5 ≈ -9 mphSo, the velocity vector in terms of i and j is approximately <15.594i - 9j> mph.