Solution
= Solution
The <Lorentz factor> for $\beta=v/c=12/13$ is
$$
\gamma=\frac1{\sqrt{1-\beta^2}}=\frac{13}{5}.
$$
The javelin's length at simultaneous barn-frame times follows from <length contraction>:
$$
\boxed{L_{\rm javelin}=\frac4\gamma=\frac{20}{13}\ \mathrm m.}
$$
Its proper length remains four metres.