2. at noon, ship a was 12 nautical miles due north of ship b. ship a was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yards) and continued to do so all day. ship b was sailing east at 9 knots and continued to do so all day. the visibility was 5 nautical miles. did the ships ever sight each other?

No

Explanation:

Let the reference origin be location of ship B in the beginning. We can then create the equation of motion for ship A and ship B in term of time t (hour):

A = 12 - 12t

B = 9t

Since the 2 ship motions are perpendicular with each other, we can calculate the distance between 2 ships in term of t

For the ships to sight each other, distance must be 5 or smaller

Since then

So our equation has no solution, the answer is no, the 2 ships never sight each other.