Another approach to velocity transformations. In Figure, reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocities of one frame relative to another with a two-letter subscript. For example, vAB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, βAB (= vAB/C) is the speed parameter corresponding to vAB.

(a) Show that

Let MAB represent the ratio (1 – βAB)/(1 + βAB), and let MBC and MAC represent similar ratios.

(b) Show that the relation

MAC = M AB MBC is true by deriving the equation of part (a) from it.

B X