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

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.

In an assembly operation illustrated in the figure, a robot moves an object __first straight upward and then also to 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 3.70 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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Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vectors in 3D concept. If you need more Vectors in 3D practice, you can also practice Vectors in 3D practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Cheney's class at RCC.