Homework 1 – SolutionCHANG1 To find thex−ycomponents of a vector, we first use the vector as the diagonalto sketch a rectangular box with its sides parallel to the coordinate axes. Then we can break upthe vector graphically to identify the components, and note that the directions of thecomponents have to match that of the vector. Specify the signs corresponding to the directionsof the components, and calculate their magnitudes using sine (opposite side) or cosine(adjacent) functions based on the triangles. Alternatively we can directly use the formulas,VxVcosandVyVsin, and note the anglemust be measured from thex-axis that islaced at the tail of the vector. The angleis positive (negative) for counterclockwise(clockwise) rotation.−Acceleration vectorarespect tox1−y1coordinates: From the figure shown we getOa= 5 m/s2x1y130°θa1ax1ay1ax1asin30∘5sin30∘2.50 m/s2ay1acos30∘5cos30∘4.33 m/s2Or usea160∘ax15cos60∘2.50 m/s2ay15sin60∘4.33 m/s2−Acceleration vectorarespect tox2−y2coordinates: From the figure shown we get
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