College of Science Physics Dept Tatsu Takeuchi Special Relativity Practice Problems 
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Addition of VelocitiesThe spacetime diagram below shows the worldlines of a tree, two cars, and two photons which all go through the origin at O; that is, they all start out from the same place at the same time (in all frames of reference). When observed from the tree frame, photon 1 is moving to the left with speed c, car 1 is moving to the left with speed c/2, car 2 is moving to the right with speed c/2, and photon 2 is moving to the right with speed c. These speeds can be read off from the spacetime diagram since in the tree frame, when the tree is at I, photon 1 is at G, car 1 is at H, car 2 is at J, and photon 2 is at K. By comparing the separation between the tree at I and photon 1 at G. and the separation between the tree at I and car 1 at H, we can conclude that car 1 is moving at half the speed of light. Similarly, by comparing the separation between the tree at I and photon 2 at K. and the separation between the tree at I and car 2 at J, we can conclude that car 2 is also moving at half the speed of light. Now let us figure out what the speeds of the tree and car 2 are when observed from the frame of reference fixed to car 1. Answer the following questions:
