At noon, ship A is 110 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

Question

At noon, ship A is 110 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer 1

f(t) = d = [(110 - 25t)² + (20t)²]^1/2; f(t) = [1025t² - 5500t + 12100]^1/2;

f'(t) = (2050t - 5500)/[2(1025t² - 5500t + 12100)^1/2]

t = 4; f'(4) = (8200 - 5500)/[2(16400 - 22000 + 12100)^1/2] = 16.744 km/h