At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

at t=5
A west of origin 20+21*5 = 125 or x=-125
B north of origin = 18*5 = 90 or y = 90
h^2 = x^2+y^2
h=(x^2+y^2)^.5 = 154 where h is hypotenuse

we want dh/dt
2 h dh/dt = 2 x dx/dt + 2 y dy/dt

2(154) dh/dt = 2(-125)(-21) + 2 (90)(18)