At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

the distance z between the ships at time t is
z^2 = (50+16t)^2 + (16t)^2
at t=z, z = 2√9697 = 196.95
2z dz/dt = 2*32(50+16t) + 32t = 1056t+3200
so, at t=7,
dz/dt = 1/2 * (7392+3200)/196.5 = 26.95 knots