Problem 2: Two spaceships are observed from Earth to be traveling in the same di

Question

Problem 2: Two spaceships are observed from Earth to be traveling in the same direction They are seen to be separated by a distance of 0.1 light-years. The pursued spaceship is seen to be traveling at a speed of 0.6c and the pursuing spaceship at a speed of 0.8c. (a) How long will it take according to a clock held by the Earth observer for the spaceships to meet up? (b) What is the speed of the pursuing spaceship as observed from the pursued spaceship? (c) How much time elapses before the spaceships meet up from the point of view of the pursued spaceship?

Explanation / Answer

2. given two spaceships A and B

travelling in same direction

apparent seperation from earth do = 0.1 LY

Va = 0.6c (pursued)

Vb = 0.8c (pursuing)

a. according to clock on earth time taken for the ships to meetup = to

to = 0.1LY/0.2c = 0.1/0.2 years = 6 months

b. speed of pursuin ship from pursued ship = v

from einstein velcoty addition

v = (Vb - Va)/(1 - VbVa/c^2)

v = 0.2c/(1 - 0.6*0.8) = 0.3846153c

c. from the point of pursued ship

distance d = do*sqrt(1 - va^2/c^2)

time t = d/v = do*sqrt(1 - 0.6^2)/0.384 c

t = 0.208 years = 2.496 months = 2 months 14 days

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