GR0877 Problem 23
PROBLEM STATEMENT: This problem is still being typed.
SOLUTION: (B) Imagine the earth ( frame, -axis is to the right and passes through the spaceships) and two spaceships approaching the earth from the left and right with equal speeds . Let’s move to the reference frame of the left spaceship (system , two systems are oriented the same way). Then, according to the velocity addition formula, the velocity of the right spaceship in this frame of reference is: , where is the velocity of the right spaceship in the frame and denotes the speed of relative to , . Thus, . But this is exactly the speed with which two spaceships approach one another (as seen from the reference frames associated with them). And we know from the length contraction formula that, if the relative speed between two frames is , a stick at rest with respect to one reference frame is observed from the other reference frame to be contracted by the factor of . The problem statement suggests . Substituting into the equation for and working with units in which :
, , or as in choice (B).
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