Car Is Traveling Along The 45o Line In S Fig. 12

A car is traveling along the 45o line in S (Fig. 12.25), at (ordinary) speed (2/√5)c.

(a) Find the components ux and uy of the (ordinary) velocity.

(b) Find the components ηx and ηy of the proper velocity.

(c) Find the zeroth component of the 4-velocity, η0. System S is moving in the x direction with (ordinary) speed √2/5c, 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 ηx and ηy in S.

(f) As a consistency check, verify that η = u/√1 – u2/c2.

A car is traveling along the 45o line in S (Fig. 12.25), at

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