On a particular day the velocity of the wind, in terms of and
, is
, where
.
and
are unit vectors in the directions East and North respectively.
To a man travelling due East the wind appears to come from a direction North West where
.
When he travels due North at the same speed as before, the wind appears to come from a direction North West where
.
Find the actual direction of the wind.
Solution:
We start by writing
.
We have two equations.
Firstly, when the man travels due East, for some constant
. We have
and so
.
We know that this, with respect to the man, is coming from North West. This means we have:
And furthermore:
.
Now consider when the man travels due North, . We have
still and so
.
We know that this, with respect to the man, is coming from North West. This means we have:
And furthermore:
,
but we have and so
,
so that .
This means that the velocity of the wind looks like:
That is the wind comes from North West. We have that
, so the answer to the question asked is N
W.
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