Answer
$29.5$ knots
Work Step by Step
Step 1. See figure: $\angle AOB=120^{\circ}$, $v_A=14$ knots, $v_b=21$ knots
Step 2. The distance between the two ships is:
$s^2=a^2+b^2-2ab\cdot cos120^{\circ}$
(The Law of the consines)
Step 3. Use $cos120^{\circ}=-1/2$ and differentiate to get $2ss'=2aa'+2bb'+ab'+a'b$
Step 4. With $a=5, b=3, s=\sqrt {25+9+15}=7, a'=v_A, b'=v_B$, we have $2(7)s'=2(5)(14)+2(3)(21)+5(21)+14(3)$ and this gives $\frac{ds}{dt}=s'=29.5$ knots
