Two ships leave a port at the same time. The first ship sails on a bearing of 40° at 18 knots and the second at a bearing of 130° at 24 knots. How far apart are they after 2 hours?

Question

Two ships leave a port at the same time. The first ship sails on a bearing of N15°W at 24 knots and the second at a bearing of N36°E at 19 knots. How far apart are they after 2 hours? (One knot is one nautical mile per hour).

Answer 1

In the 2nd part of your problem. Work out the angle between the two headings. The relative velocity will be the third side of the triangle of velocities, the magnitude of which can be obtained by the cos law: c² = a² + b² - 2abcosθ. The relative velocity times the time will be the relative displacement of the two boats.

Answer 2

The ships are moving 90 degrees apart.

18*2 = 36

24*2 = 48

Knowing the Pythagorean triangle 3-4-5, the distance apart, as 36/12 = 3 and 48/12 = 4, is 12*5 = 60 nautical miles.