1. Problem is pictured here. http://engineeringhomework.net/statics/hw1p14.html" [Broken] I have already found the x and y components, but I don't know how to get the u and v as shown.
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You would find them in exactly the same way you found x and y. To find the x component you can consider the right triangle between the force vector, the the x component and the y component. You know that the cos of the angle equals the adjacent component (the x comp in this case) divided by the hypotenuse (the magnitude of the force), and in this way you can solve for the x comp
cos Θ = A/H = x/F
Well, for the u and v, you do the same thing. You consider a right triangle, where the hypotenuse is F, the adjacent side is the u component, and the other side is a component perpendicular to u (not v). Θ is the angle between the force vector and u, in this case 21, and you can solve for u