Final answer:
It is preferable for airplanes to take off into the wind as this increases the airspeed over the wings at lower ground speeds, facilitating lift and requiring a shorter runway. The crosswind limits are usually set by the aircraft manufacturer and can be waived by the pilot in command or supervising authority.
Step-by-step explanation:
As for the crosswind limits, they are generally specified by the aircraft manufacturer and represent the maximum crosswind component under which it is safe to operate the aircraft.
The pilot in command or the supervising authority can waive these limits up to the specified aircraft limits under certain conditions.
In the given physics problem snippet, the figure illustrates how to calculate the speed and direction of the wind affecting an airplane's ground speed and trajectory.
This example reinforces the concept of how winds can alter an airplane's course and the necessity for pilots to adjust accordingly.