I think this is a situation where it's pretty important to mention the reference
frame in which the velocity is being measured. You've got two different reference
frames going on here.
-- If the plane is flying east at 395 km/hr with respect to the ground, then
that is its velocity with respect to the ground ... 395km/h east. If in addition
we know that the air is moving 55 km/h west with respect to the ground,
then the plane's velocity with respect to the air around it must be 450 km/h .
-- If the plane is flying east at 395 km/hr with respect to the air around it,
and the air in turn is moving 55 km/h west with respect to the ground, then
the plane's velocity is still 395 km/h through the air (its 'air speed'), and
340 km/h with respect to the ground (its 'ground speed').
The 'ground speed' is the vector sum of the 'air speed' and the wind speed.
There are special plastic devices made that a solo pilot can use to do this
calculation with one hand while he's flying. He can read his air speed from
a gauge in his plane, and he gets wind speed and direction for his location
by radio from air traffic control centers or flight service stations along his route.
Then he has to calculate what direction he should point the nose of his plane
in order to proceed along the ground in the direction he wants to go.
