Lydia proposes to send an interstellar probe off in stages. The first stage, tra

Question

Lydia proposes to send an interstellar probe off in stages. The first stage, traveling radially outward at 0.500c relative to Earth, will send off a second stage traveling in the same direction as the first stage at a speed of 0.500 c relative to the first stage. Finally, the second stage will send off a third stage traveling in the same direction at 0.500 c relative to the second stage. Relative to Earth, the speed of the third stage will have a magnitude of?

Please include equations/work - Thanks!

Explanation / Answer

ANSWER

Keep in mind that this is a Relativity problem. So, from theory we know that,

v = (v’ + u) / (1 + v’u/c2 )

Second Stage relative to Earth,

v = (c/2 + c/2) / (1 + (1/2)(1/2))

v = 4c/5

Third Stage relative to Earth,

v = (c/2 + 4c/5) / (1 + (1/2)(4/5))

v = 0.929c   ANS.

Regards!!!

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