Two spaceships, each 100 m long in its own rest frame, approach earth from opposite directions?

Question

with equal speeds relative to earth. As measured by a passenger in one of the spaceships, the other spaceship is 96 m long. What is the speed of the spaceships?

a) c/7
b) c/5
c)c/3
d)c/4

Answer 1

The speed of the spaceships with respect to the other is obtained from the relativistic contraction formula:

√[1-(v/c)^2] = 0.96

1 - (v/c)^2 = 0.96^2

v/c = √[1 - 0.96^2] = 1/3.5, or v = c/3.5. Since the ships are approaching each other, each one's velocity with respect to the earth will be half that, or c/7

Answer 2

how do they do it? they are looking through the earth. whoa. the approximate correct should be c because relativistic length=sqrt(1+speed^2/c^2)*original lenght

consider the spee of incoming body as negative to obtain shortening, the precise number for the stable earth and setup as above would be that ships are travelling head-on speed of 0.28c , thus everz ship is travelling 0.14c. in fact, one is travelling0.14c+1/2of earth speed the other is travelling 0.14c-1/2of earth speed.