Ship A is located 4.0 km north and 2.5 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 in unit-vector notation with toward the east? (b) Write an expression (in terms of `hatiandhatj`) for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described above. ( c) At what time is the separation between the ships least? (d) What is that least separation?

Explanation

(a) `(-32km//h)hati-(46km//h)hatj`, (b) `(2.5-3.2t)hati+(4.0-46t)hatj`, ( c) 0.084 h, (d) `2xx10^(2)m`