1. ## 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.

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

$\displaystyle \text{Find the magnitude and direction of }\overrightarrow{AB}\text{ after:}$

. . (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 . . . $\displaystyle \theta = 39^o$

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: .$\displaystyle 180^o - 39^o \:=\:141^o$

[2] Standard angle: measured CCW from due East.
. . .The standard angle is: .$\displaystyle -51^o$

[3] Heading: measured East or West of due North or due South.
. . .The heading is: .$\displaystyle S\:39^o\,E$

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