Past exam of the mathematics course of the University of Cambridge 2002 ib Paper 4 18D d Solution Created 2026-09-24 Updated 2026-10-14
In the shed frame, the leading end reaches the back when , giving . Transforming both events yieldswith every coordinate in metres. The invariant interval isThus the events are spacelike separated. Event occurs first in the shed frame, but occurs first in the javelin frame; this is allowed for spacelike separation.
In the shed frame there is a pre-impact interval during which both ends lie inside the shed, since its simultaneous moving length is only . Those simultaneous endpoint events do not remain simultaneous after a boost. In the javelin frame the front hits the back before the rear enters, and there is no simultaneous pre-impact containment of the full rod in a shed. This is rod containment and simultaneity, not inconsistent length measurements.
After impact, the front's motion changes while the rear cannot respond instantaneously: stress signals propagate no faster than light. A claim that the entire javelin stops rigidly at event is inadmissible. Actual post-impact compression or fracture needs material data and is not represented by the straight-line extrapolations in the diagrams.