A wind is blowing at 50 km h−1
from a direction 45° west of north. The pilot of an airplane wishes to fly on
a route due north from an airport. The airspeed of the airplane is 250 km h−1
.
(a)In what direction must the pilot point the nose of the airplane?
(b) What will be the airplane’s speed relative to the ground?
1
Expert's answer
2019-09-19T09:43:30-0400
Resulting aircraft speed:
v=u+w,
where u is the own aircraft airspeed, w is the wind speed.
Since wind is blowing in 45 degrees angle,
wy=wcos45°=wx=wsin45°.
Projecting the vectors on axes in absolute values:
in north(+)/south(-) axis: vy=uy−wy=ucosα−wcos45°;
in east(+)/west(-) axis: 0=ux−wx=usinα−wsin45°.
(here vx=0 because we know the aircraft in result is heading due north).
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