Optimization. At 12 noon a ship going due east at 12 knots crosses 10 nautical miles ahead
of a second ship going due north at 16 knots.
a) If s is the number of nautical miles separating the ships, express s in
terms of t (the number of hours after 12 noon).
b) When are the ships closest and what is the least distance between them

Question

Optimization.  At 12 noon a ship going due east at 12 knots crosses 10 nautical miles ahead 
of a second ship going due north at 16 knots.
a) If s is the number of nautical miles separating the ships, express s in
terms of t (the number of hours after 12 noon).
b) When are the ships closest and what is the least distance between them

anonymous · Answer

the distance would be sqrt( (12t)^2 + (10-16t)^2 ) nautical miles

differentiate and you would get t = 17/16 hours after 12 or 1 hour 3 minutes 45 seconds after 12 or 1:03:45 P.M.