Halliday, Resnick & Walker — Relativity: Problem 30

30 In Fig. 37-11, frame $S'$ moves relative to frame $S$ with velocity $0.620c \hat{i}$ while a particle moves parallel to the common $x$ and $x'$ axes. An observer attached to frame $S'$ measures the particle’s velocity to be $0.420c \hat{i}$. In terms of $c$, what is the particle’s velocity as measured by an observer attached to frame $S$ according to the (a) relativistic and (b) classical velocity transformation? Suppose, instead, that the $S'$ measure of the particle’s velocity is $-0.420c \hat{i}$. What velocity does the observer in $S$ now measure according to the (c) relativistic and (d) classical velocity transformation?