Trigonometry · Challenge problem

At noon, ship $A$ is at the origin and ship $B$ is at $(10, 0)$, with distances in km. Ship $A$ sails with constant velocity $\langle 3, 4\rangle$ km/h and ship $B$ with constant velocity $\langle -1, 2\rangle$ km/h. Find the smallest distance between the two ships, in km, in simplest radical form.