Final answer:
The question seems to mix concepts from mathematics and physics, referring to lengths and velocities, but the given information is not sufficient to calculate the length of VW without additional context or clarification regarding VW, UY, TZ, and ZW.
Step-by-step explanation:
It seems there was a typo or unclear information regarding VW, UY, TZ, ZW, as these terms do not relate to a clear mathematical context in the provided information. The latter part of the question mentions velocities and components of wind velocity given in meters per second (m/s), which suggests the topic might be related to vectors and physics rather than a simple measurement of length.
The calculation Uwx = (38.0 m/s)(-0.342) = -13 m/s describes the westward component of velocity. To find the southward component of velocity (Uwy), the given calculation uses the cosine of the angle with the horizontal, multiplied by the wind speed, and then subtracts another velocity. This is consistent with resolving a vector into its perpendicular components.
However, as the original question regarding the length of VW cannot be addressed with the given information, we are unable to provide a numerical answer without additional context or clarification. For vector magnitude, one would typically use the Pythagorean theorem to combine the perpendicular components (Vwx and Vwy) to find the magnitude of the resultant vector Vw.