At noon, ship B is $50\ \text{km}$ due east of ship A. Ship A sails north at $30\ \text{km/h}$, and ship B sails west at $40\ \text{km/h}$, as the figure shows. How close do the two ships come to each other, and when?

Fig. 1: At noon, ship A sails north at 30 km/h, and ship B, 50 km east of A, sails west at 40 km/h.