Two rocket ships, each traveling at velocity 2.00 times 10^8 m/s compared to us,

Question

Two rocket ships, each traveling at velocity 2.00 times 10^8 m/s compared to us, are moving directly opposite to each other. The rockets are each of length 103 m, as measured in their own frames. (a) What is the length of each rocket, as measured by us? _______ Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) What is the speed of one rocket, as viewed by the other rocket? _______ m/s (c) What is the length of one rocket as viewed by the other rocket? _______ m

Explanation / Answer

(A) L = L0 / Y

Y = 1 / sqrt[1 - (v/C)^2]

v = (2/3)c = 0.667c

Y = 1 / sqrt[1 - 0.667^2 ] = 1.342

L = 103 / 1.342 = 76.8 m .........Ans

(B) v = ( vA + vB ) / (1 + vA vB /c^2)

v = 0.923c

v = 0.923 x 3 x 10^8

v = 2.77 x 10^8 m/s

(C) Y = 1 / sqrt[1 - 0.293^2] = 2.6

L = 103 / 2.6

L = 39.6 m

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