A ship is sailing due north at 12 kn when it observes another ship dead at a distance of 15 n. mi. The second ship is sailing due east at 9 kn. What is the closest distance of approach of the two ships?
(0,-15) and the is at the origin.
the coordinate of the 1st boat is given by the equation
and the coordinate of the 2nd is
We can find the distance between using the pythagorean theorem.
taking the derivative we get
setting the numerator equal to zero we get
I hope this helps