= Solution
Choose event $A$, when the trailing end reaches the entrance, as $(ct,x)=(0,0)$ and as the primed origin. Write $T=ct$, $T'=ct'$. Before impact, the shed-frame <worldlines> are entrance $x=0$, back $x=1.5$, trailing end $x=0.8T$, and leading end $x=0.8T+1.2$. The <Lorentz transformation> is
$$
T'=\frac53(T-0.8x),\qquad x'=\frac53(x-0.8T).
$$
Thus in the javelin frame the ends have $x'=0$ and $x'=2$, while the entrance and back have $x'=-0.8T'$ and $x'=0.9-0.8T'$. These four lines in each frame produce the requested <spacetime diagrams>. The diagrams show initial motion; dashed portions extrapolate that motion beyond first impact and are not a model of collision dynamics.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/ib/paper-4-javelin-spacetime.png]
{title=Javelin and shed worldlines in both inertial frames, with entrance event A, first impact B and a simultaneous shed-frame containment slice}
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