The following experiment is conducted with a certain ladder and a certain barn, each of which has a rest length of 30.0 m. The barn is prepared with its left door open and its right door closed. With one farmhand standing by the front (left) door, and another farmhand standing by the back (right) door, the farmer picks up the ladder and begins runnnig towards the barn at 0.5 c. For the following questions, take the origin of the S axis to be fixed to the left side of the barn, and the origin of the S’ axis fixed to be fixed to the left side of the ladder. As usual, take the coincidence of the two origins to occur at t = t’ = 0.
(a) In the barn frame, what is the latest time t1 at which the right door may be opened without the ladder crashing into it?
(b) In the barn frame, during time 0 < t < t1 , the ladder is entirely contained in the barn. This is possible because in the barn frame, the ladder is Lorentz-contracted to a length less than that of the barn. In the ladder frame, however, the barn is Lorentz-contracted to a length less than that of the ladder. Explain then, from the perspective of the farmer, why doesn’t the ladder crash into the back door of the barn? Do a short calculation to support your conceptual discussion.