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Unformatted text preview: 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 xaxis 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 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 O a = 5 m/s 2 x 1 y 1 x 2 y 2 30° 20° θ a 2 a x 2 a y 2 20° O a = 5 m/s 2 x 1 y 1 x 2 y 2 30° 20° θ a 2 a x 2 a y 2 20° a x 2 − a sin50...
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This note was uploaded on 10/17/2009 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.
 Spring '08
 TSChang
 Physics

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