Question

At noon, ship A is 180 km west of ship B. Ship A is sailing south at 20 km/h and ship B is sailing north at 40 km/h. How fast is the distance between the ships changing at 4:00PM ? ______ km/h

Answer 1

At 4 hrs ship A is 180 W and 80 S (kilometers)

" " B is 160 N

L^2 = 180^2 + 240^2 km using Pythagorean theorem

(Note at 4 hrs L = 300 km)

L^2 = 180^2 + (20 + 40)^2 * 4^2 = 180^2 + t^2 * 60^2 distance at 4 hrs

2 L dL / dt = 2 t * 3600

dL / dt = 4 * 3600 / 300 = 48 km/hr