- #1

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**In the laboratory frame, particle 1 moves along the x-axis with a uniform velocity**

ux, and particle 2 moves along the y-axis with a uniform velocity vy. Find the

velocity of particle 2 in the rest frame of particle 1

ux, and particle 2 moves along the y-axis with a uniform velocity vy. Find the

velocity of particle 2 in the rest frame of particle 1

**Since we are looking at particle 2 in the laboratory frame from the rest frame of particle 1, I cant figure out whether or not I need to use the lorentz transform on the velocity of particle 2's speed in the y direction. It would make no sense to, as the frame in which particle 2 is moving has no motion in the y direction, and since particle 2 has no component of velocity in the x or -x direction, its component of velocity in the -x direction would be simply -ux**

Vx(p2) = -ux

Vy(p2) = vy

Vx(p2) = -ux

Vy(p2) = vy

So would not the velocity of particle 2 with respect to particle 1 simply be the square root of the sum of the squares of -ux and vy? This approach seems far too simplistic though.