Solution
= Solution
For the approaching ship, $\beta_s=0.85$ and $\gamma_s=(1-0.85^2)^{-1/2}$. Its station-frame <length contraction> gives $L_s=100/\gamma_s\,\mathrm m$. Adding the two station-frame clearances gives
$$
\boxed{L_b=100\sqrt{1-0.85^2}+4\simeq56.6783\,\mathrm m.}
$$
This is the berth's <proper length>, since the berth is at rest in the station. It is a simultaneous station-frame allocation, not a ship-frame guarantee of a safe docking maneuver.