Question

At noon, ship A is 50km due west of another ship B. Ship A is then sailing due north at 15km/h, and ship B is sailing due west at 20km/h. if these two ships continue on their respective courses, at what time will they be nearest one another, and how near?

Answer 1

Answer:

1.6hr and 30km

Step-by-step explanation:

We can consider the origin as the location of ship A at time zero. Then the coordinate of ship A would be (0, 15t) and coordinate of ship B would be (-20t+50, 0). Distance between the two ships would be √((20t-50)²+(15t)²) = 25√(t²-3.2t+4). We can find the minimum  value of the function with the help of calculus. d/dt(t²-3.2t-4) = 0 then it would be t = 1.6 . Substituting we get minimum distance as 30 km.