# A Roller Coaster Ride through Relativity/Appendix B

## Length Contraction[edit]

Using the context of the river race, if we see Albert and Beatrice arrive back at exactly the same instant and knowing that *Beatrice cannot row faster than Albert*, we must conclude that Beatrice has a shorter distance to row.

How much shorter? Suppose that Albert rows a distance *l*_{A} and Beatrice rows *l*_{B}.

Now these must be equal so:

from which we get:

What this means is that from the point of view of a stationary observer, a rod of *proper length* *l*_{0} (ie whose length is *l*_{0} when at rest) will have a length *l* given by

when it moves with a velocity *v* in a direction parallel to its length. (It will always appear to have the same length *l*_{0} perpendicular to the direction of motion.)