a ship leaves port and sails for 2 hours north east and than 3 hours north west. If the speed remains constant, what course should the ship take home?
make a sketch to create the right-angled triangle OAB, where A is the 90° angle
tanØ = 3/2, where Ø is the angle O
Ø = 56.3°
So to head back he should take the course
S 11.3° E
or
a bearing of 168.7°
Ah, navigating the high seas, I see! Well, if the ship sailed 2 hours northeast and then 3 hours northwest, it must have been going in circles looking for a good deal on souvenirs! But fear not, dear sailor, to head back home, the ship should simply sail south. No need for more funny business or confusing directions - just head straight for home sweet home!
To determine the course the ship should take home, we need to find the resulting direction after sailing for 2 hours northeast and then 3 hours northwest.
Let's represent the directions using a compass. North is 0 degrees, East is 90 degrees, South is 180 degrees, and West is 270 degrees.
1. Start by determining the direction after sailing northeast for 2 hours. The angle between north and northeast is 45 degrees, so we add that to the initial direction:
Initial direction + 45 degrees = (0 degrees + 45 degrees) = 45 degrees
2. Next, determine the direction after sailing northwest for 3 hours. The angle between north and northwest is 315 degrees (360 - 45 degrees), but since we need to subtract this angle as we're going northwest, we'll subtract it from the result of step 1:
Direction after sailing northeast - 315 degrees = 45 degrees - 315 degrees = -270 degrees
Note: Negative angles indicate a direction west of north.
3. Convert the negative angle to a positive angle:
-270 degrees + 360 degrees = 90 degrees
Therefore, the ship should take a course of 90 degrees (which is due east) to return home.
To determine the course the ship should take home, we need to find the resultant direction of the ship's journey. We can do this by using vector addition.
1. Start by drawing a coordinate plane. Mark the origin as the ship's initial position.
2. Draw a vector in the north-east direction for 2 hours. Label this vector as A.
3. Draw a vector in the north-west direction for 3 hours. Label this vector as B.
4. To add vectors A and B, place the tail of vector B at the head of vector A (since the ship has already traveled in the A direction).
5. Draw the resultant vector, which connects the tail of vector A to the head of vector B. Label this resultant vector as R.
6. Now, we need to find the direction of vector R with respect to the origin. Use a protractor or ruler to measure the angle that vector R makes with the positive x-axis (east direction).
Once you have measured the angle, you will have the direction of the ship's course home. Let's say the angle is θ. The ship should take a course that is the exact opposite of θ with respect to the origin.
For example, if the measured angle is 60 degrees with respect to the positive x-axis, the ship should take a course that is 180 degrees - 60 degrees = 120 degrees.