If a ship travels 200 km to the south and then 400 km to the west what would be the ship's displacement from its starting point?

Answer 1

If it is travelling due south and due west, then to find the displacement, we can use pythagoras' thereom because it would be a right-angled triangle.

pythagoras' thereom states that a^2+b^2=c^2

If we say that a = 200km, and b = 400km, then c^2 = 200^2+400^2

so c = (200^2+400^2)^1/2

*note that the squareroot of something is also known as being to the power of 1/2

so if we equate that,

c = 447.214km displacement from its starting point.

Since it is the displacement we are finding, we also need a direction.

To find the bearing of the point c from the starting point, because it is a right-angled triangle, we can use Tan(theta) = O/A

We know that the opposite side length (O) is 400km, and the adjacent side length (A) is 200km.

So Tan(theta) = 400/200

Now we inverse Tan it to get the angle theta.

Theta = 63 degrees 26 minutes or 63.435 degrees

Now, because it is bearings, we cannot simply just write it as 63.435 degrees, it must have a direction of North, East, South or West.

Seeing that it is in the 3rd quadrant, it is in the South-West quadrant, and so the angle is South 63 degrees 26 minutes West OR we can write it in true bearings form, and knowing that each quadrant is 90 degrees, we add the first and second quadrant, with the value we get inside our 3rd quadrant, which gives us 63"26' + 90 + 90 = 243 degrees 26 minutes True.

Finally, because this is a worded question, write a worded answer for it.

The displacement of the ship is 447.214km on a bearing of South 63 degrees 26 minutes West from the starting point.