1) Consider a particle moving with an arbitrary velocity v it does have to be constant) with respect to an inertial fram

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1 Consider A Particle Moving With An Arbitrary Velocity V It Does Have To Be Constant With Respect To An Inertial Fram 1 (36.26 KiB) Viewed 51 times

1) Consider a particle moving with an arbitrary velocity v it does have to be constant) with respect to an inertial frame of reference K. The four-vector velocity of this particle in K is then given by YE') YOU w =r vws/ where w' is the magnitude of the particle velocity with respect to Consider that itself is moving along the x-axis with constant velocity with respect to another inertial frame of reference K Assume that the Cartesian axes of K and Kare parallel and when the two origins of K and K crossed each other, the clocks were set at t = = 0. As we sow in class, the inverse Lorentz transformation of any four-vector from k into Kis given by YY00 0010 0001 where y = r.) = and VYY00 V a) Calculate the components of four-vector velocity in K, V = Now notice that the 3 Cartesian components of the ordinary velocity , can be obtained from the components of the four-vector velocity by 1 = b) Calculate v... Those are the relativistic expressions for adding" velocities . Compare those results with the (incorrect) Galilean expressions for adding velocities. c) If -39) and v, = 0.6c, what is the magnitude of v=+o+e3 0.9 0 0 2 d) If w - and +, = 0.6c, what is the magnitude of v= g++写?