hw1solution - CHANG 1 To find the x y components of a...

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Homework 1 – Solution CHANG 1 To find the x y components of a vector, we first use the vector as the diagonal to sketch a rectangular box with its sides parallel to the coordinate axes. Then we can break up the vector graphically to identify the components, and note that the directions of the components have to match that of the vector. Specify the signs corresponding to the directions of 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, V x V cos and V y V sin , and note the angle must be measured from the x -axis that is laced at the tail of the vector. The angle is positive (negative) for counterclockwise (clockwise) rotation. Acceleration vector a respect to x 1 y 1 coordinates: From the figure shown we get O a = 5 m/s 2 x 1 y 1 30° θ a 1 a x 1 a y 1 a x 1 a sin30 5sin30 2.50 m/s 2 a y 1 a cos30 5cos30 4.33 m/s 2 Or use a 1 60 a x 1 5cos60 2.50 m/s 2 a y 1 5sin60 4.33 m/s 2 Acceleration vector a respect to x 2 y 2 coordinates: From the figure shown we get
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