Thread: Vectors question

Two ships, A & B, leave port O simultaneously. Ship A travels due north at 16km/h and ship B travels due east at 13km/h.
Find the magnitude & direction of AB after:
(i) 1 hour (ii) 3 hours (iii) t hours.

There are more parts to this question which I may post later. This is pretty simple but the answer in the book for all parts gives direction as 141 degrees.
I got an answer of 39 degrees from A. Is this acceptable or must answer be given as 141? I understand that 180-39 = 141, but I don't understand even why 141 is an acceptable answer. I have drawn quadrants and everything and just don't understand where it comes from and why...?

If anyone could answer it would be appreciated.
Thanks.

Hello, BenLaden!

Two ships, and , leave port O simultaneously.
Ship travels due north at 16 km/h and ship travels due east at 13km/h.



. . (i) 1 hour . . (ii) 3 hours . . (iii) t hours.

The answer in the book gives the direction as 141°.
I got an answer of 39° from A.
Is this acceptable or must answer be given as 141° ?

After one hour, we have this diagram:

Code:

    A *
      |\
      | \
      |θ \
   16 |   \
      |    \
      |     \
      |      \
    O * - - - * B
         13

You are correct . . .

But information is useless unless it is clear where the angle is located.


There are several methods for indicating the direction.
Here are a few of them.

[1] Bearing: measured clockwise from due North.
. . .The bearing is: .

[2] Standard angle: measured CCW from due East.
. . .The standard angle is: .

[3] Heading: measured East or West of due North or due South.
. . .The heading is: .


The problem should have stated the method of indicating the direction.