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?
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
To solve this problem, we need to break it down step by step and use some basic trigonometry and geometry concepts. Let's start with the first part:
a) What is the new bearing?
To find the new bearing, we need to determine the angle the ship has turned from its initial bearing of 100 degrees. Since the ship turned 90 degrees toward the south after 1 hour, we can subtract this angle from the initial bearing.
New bearing = Initial bearing - Angle turned
New bearing = 100 degrees - 90 degrees
New bearing = 10 degrees
Therefore, the new bearing is 10 degrees.
Now, let's move on to the second part:
b) After 2 hours, maintaining the same speed, what is the bearing of the ship from the port?
To find the bearing of the ship from the port after 2 hours, we need to calculate the total angle turned by the ship. Since the ship turned 90 degrees toward the south after 1 hour and maintains the same course for the next hour, the total angle turned is 90 degrees + 90 degrees = 180 degrees.
We can then add this angle to the new bearing we calculated in part a to find the final bearing.
Final bearing = New bearing + Total angle turned
Final bearing = 10 degrees + 180 degrees
Final bearing = 190 degrees
Therefore, the bearing of the ship from the port after 2 hours is 190 degrees.
Remember, in this problem, we assumed that the ship maintains a constant speed and the turns are instantaneous.