Ted and Mary are playing a game of catch in frame S\', which is moving at 0.400c

Question

Ted and Mary are playing a game of catch in frame S', which is moving at 0.400c with respect to frame S, while Jim, at rest in frame S, watches the action (Fig. P9.50). Ted throws the ball to Mary at 0.860c (according to Ted), and their separation (measured in S') is 1.90 1012 m. (a) According to Mary, how fast is the ball moving? (b) According to Mary, how long does it take the ball to reach her? (c) According to Jim, how far apart are Ted and Mary? (d) According to Jim, how long does it take the ball to reach Mary?

Explanation / Answer

a)v=0.860c m/s

d0=1.9*10^12m ted and mery are in the same frame

b)t=d/v=1.9*10^12/0.86*3*10^8=0.736*10^6 s

c)d=d01-v^2/c^2=1.9*10^12(1-0.16)=1.74^10^12m

d)t=1.74*10^12/0.4*3*10^8=1.45*10^6 s

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