Solved: Another approach to velocity transformations. In

Chapter 37, Problem 65

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Another approach to velocity transformations. In Fig. 37-31, reference frames Band 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, v AB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, f3AB (= v AB/C) is the speed parameter corresponding to VAB. (a) Show that f3AC = f3AB + f3BC . 1 + f3ABf3BC Let MAB represent the ratio (1 - f3AB)/(l + f3AB)' and let M Bc and MAC represent similar ratios. (b) Show that the relation MAc = MABMBc is true by deriving the equation of part (a) from it.

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