Question

Ships A and B leave port together. For the next two hours, ship A travels at 10 mph in a direction 25° west of north while the ship B travels 25° east of north at 40 mph.

(a) What is the distance between the two ships two hours after they depart? (answer in miles)

(b) What is the speed of ship A as seen by ship B?
(answer in mph)

Answer 1

Right down an equation for each ship showing its position in Cartesian coordinates:
r1(t) = (x1(t), y1(t))
r2(t) = (x2(t), y2(t))

Then the distance between them at t = 2 hours will be:

| r1(2) - r2(2) | = sqrt( (x2(2) - x1(2))^2 + (y2(2) - y1(2))^2 )

and their relative velocity

r2'(t) - r1'(t) or vice versa
where ' = d/dt