A spaceship of rest lenght 130 m is traveling at a constant speed of 0.7c with r

Question

A spaceship of rest lenght 130 m is traveling at a constant speed of 0.7c with respect to the Earth. A small meteorite, travelling in the same direction at a constant speed of 0.9c relative to the spaceship, passes by the spaceship.

a. Using a laser gun mounted on the back of the spaceship, the captain of the spaceship fires a light pulse at the meteorite as it passes the front of the spaceship. According to the captain, how far from the front of the spaceship will the meteorite be when it is hit by the light pulse?

Explanation / Answer

For the spaceship: Lo = 130 m; v1 = 0.7c

For the meteorite: v2 = 0.9c

Lenght contraction equation : L = Lo (1 - v2/c2)1/2

and the velocity: v' = v1 + v2 / 1 + v1xv2/c2

so v' = (0.9c + 0.7c) / 1 + (0.7cx0.9c)/c2

v' = 0.9816c

L = 130 [(1 - 0.98162)1/2

L = 24.82 m

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