🤓 Based on our data, we think this question is relevant for Professor Schulte's class at UCF.

In an assembly operation illustrated in the figure, a robot moves an object **first straight upward** **and then also t****o the east around an arc** forming **one-quarter of a circle** of **radius 4.80**** cm** that lies in an east-west vertical plane. The robot then moves the object **upward** and to the **north** through **one-quarter of a circle of radius 3.7****0 cm** that lies in a north- south vertical plane. Find (a) the **magnitude of the total displacement** of the object and (b) the **angle** the total displacement makes with the **vertical**.

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We're looking for the **resultant displacement** of an object moved in two separate steps by an assembly machine.

When adding vectors in 3D, the steps are basically the same as adding vectors in 2D, except that drawing diagrams for 3D problems is often skipped because it's more complicated to do.

- Resolve the vectors into
**components**, if necessary. **Organize**your known information.**Add or subtract**vectors as required.- Convert back to
**magnitude-angle notation**(unless the problem only asks for components).

For step 1, we'll usually use equations of this form to find our components when the components aren't given to us:

$\overline{){{\mathit{A}}}_{{\mathit{x}}}{\mathbf{=}}\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}{\mathbf{cos}}{\mathbf{}}{\mathit{\alpha}}}$, $\overline{){{\mathit{A}}}_{{\mathit{y}}}{\mathbf{=}}\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}{\mathbf{}}{\mathbf{cos}}{\mathbf{}}{\mathit{\beta}}}$, $\overline{){{\mathit{A}}}_{{\mathit{z}}}{\mathbf{=}}\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}{\mathbf{cos}}{\mathbf{}}{\mathit{\gamma}}}$

For step 4, we'll use the same equations from step 1 solved for *α*, plus the equation for magnitude:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{A}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{A}}_{\mathit{y}}}^{\mathbf{2}}\mathbf{+}{{\mathit{A}}_{\mathit{z}}}^{\mathbf{2}}}}$

This problem looks tricky at first because it's very wordy! But let's tackle it one piece at a time.

Vector Addition & Subtraction

Vector Addition & Subtraction

Vector Addition & Subtraction

Vector Addition & Subtraction