At noon ship A is 20 nautical miles due west of ship B Ship
At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 17 knots. How fast is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
Solution
at 5 A is at 20+5*17 x=105 west B is at 17*5 y=85 d=sqrt(x^2+y^2) d(d)/dt=(x*dx/dt+y*dy/dt)/(sqrt(x^2+y^)) =(105*17+85*17)/sqrt(105^2+85^2) =23.9 knots
