Determine the component of the displacement vector

Question

Assignment:

Question

1. A displacement vector Overscript right-arrow EndScripts in the xy plane is 52 m long and directed at angle θ = 22° in the figure. Determine (a) the x component and (b) the y component of the vector.

2. In the figure, a heavy piece of machinery is raised by sliding it a distance d = 17.7 m along a plank oriented at angle θ = 37.8 ° to the horizontal. How far is it moved (a) vertically and(b) horizontally?

3. Find the (a) x, (b) y, and (c) z components of the sum Overscript right-arrow EndScripts of the displacements Overscript right-arrow EndScripts and Overscript right-arrow EndScripts whose components (in meters, m) along the three axes are c_x = 3.9, c_y = -4.3, c_z = -6.5; d_x = 4.3, d_y = -1.9, d_z = 3.3.

4. For the vectors a Overscript right-arrow EndScripts equals left-parenthesis 3.0m right-parenthes Overscript ^ EndScripts plus left-parenthesis 4.0m right-parenthesis Overscript ^ EndScripts and Overscript right-arrow EndScripts equals left-parenthesis 5.0m right-parenthesis Overscript ^ EndScripts plus left-parenthesis negative 2.0m right-parenthesis Overscript ^ EndScripts, give a Overscript right-arrow EndScripts plus Overscript right-arrow EndScripts in (a) unit-vector notation, and as (b) a magnitude and (c) an angle (relative to Overscript ^ EndScripts in the range of (-180°, 180°]). Now give Overscript right-arrow EndScripts minus a Overscript right-arrow EndScripts in (d) unit-vector notation, and as (e) a magnitude and (f) an angle (relative to Overscript ^ EndScripts in the range of (-180°, 180°]).