The Overloaded Liberty Boat
A ship's liberty boat is rated for a maximum load of 2,500 kg (passengers plus cargo). Each sailor is assumed to weigh 75 kg, and personal gear adds 10 kg per person. The boat must ferry 24 sailors ashore along with 300 kg of mail and supplies. The coxswain also notes that the boat's hull displaces water such that every 100 kg of extra load lowers the freeboard by 1.5 cm, and regulations require at least 30 cm of freeboard. With no load beyond the boat's own structure, freeboard is 55 cm. The coxswain must decide whether to make one trip or split the load, and how that choice affects freeboard safety.
1. Compute the total load for a single trip and check it against the 2,500 kg rating.
Read the worked answer
Per sailor: 75 kg body + 10 kg gear = 85 kg. 24 sailors = 24 × 85 = 2,040 kg. Add supplies 300 kg → total = 2,340 kg. 2,340 kg ≤ 2,500 kg, so the single trip is within the weight rating by 160 kg.
2. Using the freeboard data, determine whether the single trip meets the 30 cm freeboard rule.
Read the worked answer
Load = 2,340 kg. Freeboard loss = (2,340 / 100) × 1.5 cm = 23.4 × 1.5 = 35.1 cm. Freeboard remaining = 55 − 35.1 = 19.9 cm. Required minimum = 30 cm. 19.9 cm < 30 cm, so the single trip violates the freeboard rule even though it passes the weight rating. The binding constraint is freeboard, not mass.
3. Recommend a two-trip split and verify it satisfies both the weight and freeboard limits.
Read the worked answer
Split 12 sailors per trip plus 150 kg supplies. Load per trip = 12 × 85 + 150 = 1,020 + 150 = 1,170 kg (well under 2,500 kg). Freeboard loss = (1,170 / 100) × 1.5 = 11.7 × 1.5 = 17.55 cm. Freeboard remaining = 55 − 17.55 = 37.45 cm ≥ 30 cm. Both limits satisfied. The two-trip plan is the correct call; the coxswain must trade time for freeboard safety.