Ship A is sailing due west at 8km/hr when it sees ship B northwest of its present position. If ship B is sailing due south at 3km/hr, then how close will they come on their courses?

Answer 1

It depends on how far away B is when sighted. If it is k km north and west, then the distance z between the ships after t hours is

z^2 = (k-3t)^2 + (k-8t)^2
= 73t^2-22kt+k^2

dz/dt = (73t - 11k)/√(73t^2-22kt+k^2)

dz/dt=0 when t = 11k/73
so, the minimum distance is

z = 5k/√73