Question in Calculus

Question

At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 6 PM?

The distance is changing at?

Answer 1

Let f(t) is square of distance between ships. Then f(t) = [D(t)]²= (50 + 20t)² + (18t)²; f'(t) = 2D·D' =

40(50 + 2t) + 36t = 2000 + 116t; D' = (1000 + 58t)/√[(50 + 20t)² + 324t²] = (1000 + 58·6)/√[(50 + 120)² +

324·36] = 6.693 knot/h