- #1

MikeLizzi

- 240

- 6

## Homework Statement

Given

Space Time Coordinate of object <t, x, y, z> = <0, 0, 0, 0>

Velocity of object as Vector <betaX, betaY, betaZ> = <.866, 0 ,0>

Velocity of target reference frame as Vector <betaX, betaY, betaZ> = <-.866, 0 ,0>

Transform velocity of object to the target reference frame using the 4-vector technique.

## Homework Equations

## The Attempt at a Solution

[/B]Following directions from a source on the internet...

Velocity as a 4-vector (tau, vx, vy, vz)

= <1, betaX, betaY, betaZ>

= <1, 0.866, 0.0, 0.0>

magnitude of 4-vector

= Sqrt( 1 + betaX * betaX + betaY * betaY + betaZ * betaZ )

= 1.3228590249909473

Velocity as a 4-vector normalized (tau, x, y, z)

= <1/magnitude, betaX/magnitude, betaY/magnitude, betaZ/magnitude>

= <0.7559384493044097, 0.6546426970976188, 0.0, 0.0>

Transform the 4-vector where L is the Lorentz Transform populated for the target velocity:

v' = Lv

resulting in v'(tau, x, y, z)

= <2.6454852575216505, 2.6183403845739543, 0.0, 0.0>

? I should be getting a vx value somewhere around .98c. Totally lost.