Another approach to velocity transformations. In Fig. 37-31, 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, ßAB (= vAB/c) is the speed parameter corresponding to vAB (a) Show that
Let MAB represent the ratio (1 − ßAB)/(1 + ßAB), and let MBC and MAC represent similar ratios. (b) Show that the relation
MAC = MABMBC
is true by deriving the equation of part (a) from it.
Figure 37-31 Problem 65, 66 and 67.
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