Let us consider a moving object O on a moving frame. Suppose S is a moving frame with relative velocity u > 0 from S and S is another moving frame with v > 0 from S: x y z S x y z S ut (a) Write down the Lorentz transformation between S and S. (b) Solving x = 0 in S, find the motion equation of O in S. (c) Let us observe S from S: x y z S x y z S vt Write down the Lorentz transformation between S and S. (d) Combine the above results to build the Lorentz transformation between S and S. (e) With this Lorentz transformation between S and S, conclude that no one can exceed the speed of light c by adding 0 < u < c and 0 < v < c.