Two ships leave from the same port. One ship travels on a bearing of 157º at 20 knots and the other on a bearing of 247º at 35 knots. After 8 hours calculate the bearing of the second ship from the first, to the nearest minute.
(1 knot is a speed of 1 nautical mile per hour).
The first ship travels with a bearing of 157 degrees at 20 knots. Let the bearing be with respect to a ray pointing towards the east. After 8 hours the ship has traveled 20*8*cos (157) towards the east and 20*8*sin (157) towards the north.
Solving, we get the position of the ship as 147.28 nautical miles west and 62.51 miles north.
Similarly, the position of the second ship is 35*8*cos (247) towards the east and 35*8*sin (247) towards the north.
This gives the position of the ship as 109.4 miles towards the west and 257.74 miles towards the south.
The distance between the two ships is sqrt[(147.28-109.4)^2+(62.51+257.74)^2] = 322.48 miles.
The bearing of the second ship is 247-157 = 90 degrees with respect to the first.
The bearing of the second ship is 90 degrees with respect to the first and it is 322.48 miles away from it after 8 hours.