Measure a real vector

In the classroom are many Post-It notes with different letters. Your job is to determine the displacement between one pair of notes, in the sense

       Vector D  =  A - B

 

You should use a coordinate system involving the directions

• x-axis: East positive, West negative
• y-axis: North positive, South negative
• z-axis: up positive, down negative

Express your result in meters. Don't forget to include the uncertainty in each component! You should make a table that looks like this:

           Length of vectors in meters

vector     x-coord      y-coord     z-coord      magnitude
-----------------------------------------------------------

  A    3.24 +/- 0.12

  B

 A-B

When you are finished, you should have

1. a map on graph paper showing a top-down view of your two endpoints, and all the intermediate measurements you made
2. a map on graph paper showing a plan view looking north of your endpoints, and all the intermediate measurements you made
3. a neat set of all calculations, working out the uncertainty in each component
4. calculations showing the magnitude of the vector, plus its uncertainty

   Bonus!

5. calculations showing the directions (North of East, up from East) of the vector, plus their uncertainties

You may find it handy when dealing with uncertainties to refer to

• Prof. Lindberg's guide to uncertainties. Check out the section on propagation of errors.
• My guide to uncertainties, which also describes the propagation of errors.
• Ultra-condensed description of propagation of errors.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.