Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, each with a speed 0.50c relative to Earth. As measured by a passenger in one of the spaceships,
How long is the other spaceship?
A) 70 m
B) 60 m
C) 80 m
D) 50 m
E) 90 m

Question

Quizplus · Accepted Answer

The length contraction formula is L = L0 * sqrt(1 - v^2/c^2). Here, L0 = 100 m and v = 0.50c. Plugging in these values, L = 100 * sqrt(1 - (0.50)^2) = 100 * sqrt(0.75) = 100 * 0.866 = 86.6 m. However, since the observer is in one of the spaceships, the relative speed is higher due to relativistic velocity addition, making the contracted length 60 m.

Two Spaceships, Each 100 M Long in Its Own Rest