2. Consider frame S ' moving along the positive a: direction with speed 1: relative to 8. \"re know how to trans- form between the :r and y coordinates on S, to the :r' and y' coordinates on 3' Similarly, we know how to transform between the horizontal component of the speed of an object on 3 given by it,\" and the horizontal component of the speed of an object on Sr given by 11; {a} Derive the respective Lorentz transformations for t and t' (b) Show that try, the vertical component of the speed of an object relative to S, transforms to 11; relative to 3' according to: P 2 \"v y 1'\" {1 urn/c2)\" where or is the horizontal component of the velocit;r of the object relative to S, and Tu is the rela- '11. tivistic factor between the two frames 3 and S