Summarizing Addition of Velocities

Summary

• Velocities in two dimensions are added using the same analytical vector techniques, which are rewritten as
  \({v}_{x}=v\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta \)
  \({v}_{y}=v\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \)
  \(v=\sqrt{{v}_{x}^{2}+{v}_{y}^{2}}\)
  \(\theta ={\text{tan}}^{-1}\left({v}_{y}/{v}_{x}\right).\)
• Relative velocity is the velocity of an object as observed from a particular reference frame, and it varies dramatically with reference frame.
• Relativity is the study of how different observers measure the same phenomenon, particularly when the observers move relative to one another. Classical relativity is limited to situations where speed is less than about 1% of the speed of light (3000 km/s).

Glossary

classical relativity

the study of relative velocities in situations where speeds are less than about 1% of the speed of light—that is, less than 3000 km/s

relative velocity

the velocity of an object as observed from a particular reference frame

relativity

the study of how different observers moving relative to each other measure the same phenomenon

velocity

speed in a given direction

vector addition

the rules that apply to adding vectors together

Also Read:

Relative Velocity

Relative Velocities and Classical Relativity