Question

Ships A and B leave port together. For the next 4 hours, ship A travels at 35 mph in a direction 40 degrees east of north while ship B travels 70 degrees north of west at 25 mph. What is the distance, in mi, between the two ships 4 hours after they depart?

Answer 1

Turn them into vectors (calculate each one's x and y speed) and subtract A from B

Turn the resultant vector into a speed and direction

Ship A
x = 35 x sin(320) = -22.49 mph
y = 35 x cos(320) = 26.81 mph

Ship B
x = 25 x sin(70) = 23.49 mph
y = 25 x cos(70) = 8.55 mph

B - A:
x = 23.49 - (-22.49) = 45.98 mph
y = 8.55 - 26.81 = -18.26 mph

Relative speed = sqrt ( x² + y²) = sqrt (45.98² + 18.26²) = 49.473 mph

Distance between two ships after 4 h = 49.473*4 = 197.89 miles

Spedd of Ship A as seen by B = 49.473 mph