SOLUTION: A ship that can cruise at 65 km/h in still waters, set course south-west. It is driven off course by a current flowing W 21° N at a rate of 16 km/h. Calculate the resultant vel

Question 1161657: A ship that can cruise at 65 km/h in still waters, set course south-west. It is driven off course by a current flowing W 21° N at a rate of 16 km/h.
Calculate the resultant velocity in magnitude and direction
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The way I understand the problem the ship started going south-west in still water, which I would represent like this:

I would decompose the ship-still water velocity vector
into components in the x- and y-directions:
and .

According to my understanding directions are given as angles measured clockwise from North,
or as acute angles from the North or South directions, with N or S followed by the angle and then the direction.
In the second case,

would mean a direction forming a angle from North in the direction of West, like this

However, the

in this problem may mean a angle from West in the direction of North, like this

In that case the x- and y-components of the current vector are
and ,
and the situation would look like this

Then, the components of ship resultant velocity vector would be
and .
A way to calculate the magnitude of that resultant is using the Pythagorean theorem

The angle if forms with the x-axis is such that
, which corresponds to
If the current was designated as

because it was North from West,
then is South from West,
and should be called

.
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