(a) In Ex. 12.6 we found how velocities in the x direction transform when you go from S...

(a) In Ex. 12.6 we found how velocities in the x direction transform when you go from S to .Derive the analogous formulas for velocities in the y and z directions.

(b) A spotlight is mounted on a boat so that its beam makes an angle with the deck (Fig. 12.20). If this boat is then set in motion at speed v, what angle θ does an individual photon trajectory make with the deck, according to an observer on the dock? What angle does the beam (illuminated, say, by a light fog) make? Compare Prob. 12.10.

Reference problem 12.10

A sailboat is manufactured so that the mast leans at an angle with respect to the deck. An observer standing on a dock sees the boat go by at speed v (Fig. 12.14). What angle does this observer say the mast makes?