Owen and Dina are at rest in frame S\', which is moving with a speed of v1 = 0.5

Question

Owen and Dina are at rest in frame S', which is moving with a speed of v1 = 0.590c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (see figure below). Owen throws the ball to Dina with a speed of v2 = 0.830c (according to Owen) and their separation (measured in S') is equal to d = 1.95 1012 m. (a) According to Dina, how fast is the ball moving? .83 c (b) According to Dina, what time interval is required for the ball to reach her? 7831.3 c (c) According to Ed, how far apart are Owen and Dina? ?????

Explanation / Answer

v = 0.570 c

Ub' = -0.810 c

delta x' = 1.75 x 1012 m.

a) According to dina Ub?' = -0.810 c

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b) delta t = delta x' / Ub?'

= 1.75 x 1012 / (0.810 * 3 * 108) = 7202 s

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c) delta x = sqrt(1 - 0.5702) * 1.75 x 1012

= 1.44 x 1012 m

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d) Ub = Ub' + v / 1 + (Ub' * c2)

= -0.810 + 0.57 / (1 + (-0.810*0.570) )

= -0.44 c [the ball move slower ]

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