Walker, Halliday & Resnick — Motion in Two and Three Dimensions: Problem 81

81 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 \(\hat{i}\) toward the east? (b) Write an expression (in terms of \(\hat{i}\) and \(\hat{j}\)) 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?