3. Two ships \(A\) and \(B\) are sailing in the same direction at constant speeds of \(12 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and \(16 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) respectively. They are sailing along parallel lines which are 4 km apart. When the distance between the ships is \(4 \mathrm {~km} , B\) turns through \(30 ^ { \circ }\) towards \(A\). Find the shortest distance between the ships in the subsequent motion.