Ship A is located 3.2 km north and 2.1 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east.
(a) What is the velocity of A relative to B (Express your answer in terms of the unit vectors i hat bold and j hat bold, where i hat bold is toward the east.)
(b) Write an expression (in terms of i hat bold and j hat bold) for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described as above.
(c) At what time is the separation between the ships least?
(d) What is that least separation?