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 0.500 c 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:

a) 0.500c

b) 0.800c

c) 0.929c

d) 0.972c

e) 1.500c

I need help trying to understand this, and I'd prefer if there was some notation to the velocities so that I can better understand the order of progression for the answer.

Explanation / Answer

option c is correct

velocity of second stage wrt earth

v = (v’ + u)/(1 + v’u/c2 )

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

velocity of third stage wrt earth,

v = (c/2 + 4c/5)/(1 + (1/2)(4/5)) = 0.929c

option c is correct

v' is the relative velocity of second stage with respect to first stage and u is the velocity of first stage (for first equation) ....this equation is used twice....the other time for second and third instead of first and second in equation

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