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)50 m
B)60 m
C)70 m
D)80 m
E)90 m

Question

Quizplus · Accepted Answer

The length contraction formula is $L = L_0\sqrt{1 - v^2/c^2}$, where $L_0$ is the rest length, $v$ is the relative velocity, and $c$ is the speed of light. For a spaceship moving at 0.50c, the length as observed from the other spaceship, taking into account the relativistic velocity addition formula for the effective velocity between the spaceships, is contracted to 60 m. This is because the effective velocity is not simply $0.50c + 0.50c$ due to relativistic effects, but the calculation simplifies since the question only requires recognizing that length contraction occurs, and the given options suggest a basic understanding that the length will be contracted, with 60 m being the correct calculation for a length contraction scenario at the given speed.

Two Spaceships,each 100 M Long in Its Own Rest Frame,approach