1. The problem statement, all variables and given/known data Consider a frame that is moving with velocity v in the positive x-direction. An observer in this moving frame measures the velocity of the particle in the x- and z-direction, u_x' = 0.9c, u_z'=0 a) What is the maximum velocity of the particle in the y-direction u_y' measured by the observer in the moving frame? b) What velocity components does an observer in a frame at rest measure in the x-, y- and z-direction for v = 0.5c 2. Relevant equations v(t) = v_x(t) + v_y(t) + v_z(t) u_x' = u_x - v / (1-(v/c^2) u_y' = u_y / (gamma_v (1-(v/c^2) * u_x) u_z' = u_z / (gamma_v (1-(v/c^2) * u_x) gamma_v = 1 / sqrt(1-(v/c^2)) 3. The attempt at a solution I am not sure but I thought the first equation can be used, so it would be 0.9 + 0 + u_y' = 1, then solve for u_y' ? so u_y' = 0.1c ?? and for part b) , I use the values of u_x', u_y' and u_z', with the given value of v = 0.5c in the equations, to solve for u_x, u_y and u_z, but I'm not sure do I plug in the v as 0.5c, or use the actual speed of light 0.5*3*10^8 ?