A car is traveling along the 45o line in S (Fig. 12.25), at (ordinary) speed (2/â5)c.
(a) Find the components ux and uy of the (ordinary) velocity.
(b) Find the components Î·x and Î·y of the proper velocity.
(c) Find the zeroth component of the 4-velocity, Î·0. System S is moving in the x direction with (ordinary) speed â2/5c, relative to S. By using the appropriate transformation laws:
(d) Find the (ordinary) velocity components ux and uy in ,S.
(e) Find the proper velocity components Î·x and Î·y in S.
(f) As a consistency check, verify that Î· = u/â1 â u2/c2.