An airplane traveling to the northwest is exerting just enough force to overcome wind resistance. It encounters a sudden wind gust which is directed at 30 degrees south of east, which results in a net force in that direction.
-
During the half-second before the pilot has time to react to the gust, does the airplane speed up, slow down or maintain constant (or very nearly-constant) speed?
On a coordinate system with y directed to the north and x to the east, the northwest direction would be at 135 degrees. The direction of the wind is 30 degrees south of east, which would be 30 degrees clockwise from the positive x axis, at angle 330 degrees.
A sketch will show that the wind is mostly in the direction opposite the airplane's motion, and will therefore exert a force which is mostly in the direction opposite motion. This will slow the plane.
-
Does it veer a bit to the right, a bit to the left or does it continue traveling along a straight line?
The wind direction is 330 degrees. The direction opposite the airplane's motion is 135 deg + 180 deg = 315 degrees. To get from 315 deg to 330 deg requires a 15 deg rotation in the positive, or counterclockwise, direction. To move directly 'into' the wind the airplane would have to head at 330 deg - 180 deg = 150 deg, which from the point of view of the pilot would be 15 degrees to the left of the 135 degree heading.
At the 135 deg heading the wind is therefore perceived to be blowing directly mostly in direction of the airplane's motion, but also somewhat to the right.
Thus the wind will slow the airplane and cause it to veer toward the right.<h3>In terms of vectors, the wind makes an angle of 195 degrees, as measured counterclockwise from the original direction of motion.
The figure below depicts the airplane's direction of motion (135 degrees relative to the easterly direction) and the direction of the gust (330 degrees relative to the easterly direction). It's obvious that the wind is in a direction which is mostly opposite the direction of motion. Though it's obvious from this sketch that the component of the wind's velocity perpendicular to the velocity of the airplane will be perceived as toward the right, we can't rely on sufficiently on the accuracty of our sketch, so we have to figure out the relevant angles to be sure.
University Physics Students Note:
The component of the wind velocity in the direction of motion is
wind component in direction of motion = wind velocity * cos(195 deg) = -.97 * wind velocity
while the component perpendicular to the direction of motion is
wind component perpendicular to direction of motion = wind velocity * sin(195 deg) = -.26 * wind velocity.
