Question

I've attempted this problem a few times but I can't get the right answer. Can someone show me how I can do it?

A ship leaves the port of Miami with a bearing of 100 degrees and a speed of 15 knots. After 1 hour, the ship turns 90 degrees toward the south.

a) what is the new bearing
b) after 2 hours, maintaining the same speed, what is the bearing of the ship from the port?

Answer 1

Landlubber mathematicians have never been to sea :(
The direction a ship is heading is called "heading"
The direction the ship is from you is called its "bearing".
That aside:
from origin go 15 nautical miles at 90 + 10 degrees clockwise from North, or 10 degrees South of East.
Now turn 90 degrees toward South, which gives you a heading 10 degrees West of South (190 degrees heading), go 30 Nautical miles.
So my East components are:
15 cos 10 - 30 sin 10
= 9.56
And my South components are:
15 sin 10 + 30 cos 10
=32.1
So the tangent of my angle from the South axis from the origin is
tan (angle) = 9.56/32.1 = .298
so
angle east of south = 16.6 degrees
However for our bearing from the origin we want clockwise from North
180 - 16.6 = 163.4